Author Name:
Prentice Hall General Reference Travel

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Prentice Hall General Reference Travel

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CORPORATE General Electric Company

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... you'll become an expert with your Magic Cap communicator!<p> <b> General Magic, Inc.</b> formed an alliance that includes Apple, Sony, Motorola, ...

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General Magic Inc. Staff

AKA names:
General Magic Inc Staff

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CORPORATE United States General Accounting Office

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United States General Accounting Office

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C United States General Accounting Office

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CORPORATE United States General Accounting Office

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... PressE-Commerce DevelopmentsBuilding on Broadband – With the RightBusiness Model1Colleen Arnold General Manager, Global Communications Sector, IBM1. Introduction Broadband as the Next ... convergence transformationfor service providers because it is a stepping-stone tooffering next-generation services and transitioning net-works to become completely IP-based.Content services will ... creating new growth for all.This convergence process – both in terms of voice,video and data; and across mobile, wireless and fixedline ...
... broadband offer-ing, since it’s a legitimate revenue opportunity in theshort term and improves customer profitability in thelong term. .3. On Demand Business Model forTelecommunicationsMore competition in the broadband ... its future costs by morethan $1 billion over the eight-year term and en-hance its revenues through the deployment of newwireless data ... the seven largest mobileproviders. . .” in the US.3. Meeting new-generation needs with next-genera-tion networksThe network plays a crucial role in ... billing, are placing greater demands on theirproviders’ legacy networks.IP-based, next generation networks give providersthe flexibility to provide services on demandthrough a ...
... positioned tooffer a superior broadband offering to end-consumers.– In the short-term, , broadband strategy is about find-ing new revenue streams to ... to spur the next phase ofgrowth in telecom– In the long-term, , broadband teaches serviceproviders valuable lessons of the mechanics ofemerging ...

Author Name:
Colleen Arnold General Manager, Global Communications Sector, IBM

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... within a forum and across forums.The first gives a direct measure of performance on the task wetrained the classifier to do. ... task wetrained the classifier to do. The second gives a measurement of howwell the classifier would generalize to an unseen forum in the samelanguage. For Antichat, in ... World, Hell or Darkode. These results allindicate that the classifier generalizes well and analysts could useit in the future on other, ...
... (140 posts, 4 annotators per post)We used the Fleiss Kappa measurement of inter-annotator agree-ment [Fleiss 1971] and found that our annotations ... with noun phrases as the fundamental units of prod-ucts. We generalize ground-truth noun phrases from our headwordannotation according to the output ... identification scheme. If all we want todo is identify the general product composition of a forum, then wedo not need to ... system-predicted positives), recall (true pos-itives over ground truth positives), and F-measure (F1, theharmonic mean of precision and recall).• Performance on recovering ...
... Cross-forum evaluation of the post-level product extractor.We report product type F-measure on the test sets for three variantsof the post-level system: ... as well on these due to having never seen therelevant terms before. In experiments, we found that our extractorwas roughly twice ...
... Our approach uses natural language processing and machinelearning to automatically generate high-level information about un-derground forums, first identifying posts related to ...
... Complete Dump German May 2007–Nov 2009 120,560 (30.83%) 18,834Table 1: General properties of the forums considered.Non-English Forums. We analyzed three non-English ...
... to varia-tion in language as well as forum, though to generalize to furtherlanguages would require additional labeled data.4.1.4 Limitations.We investigated why ... considered did notimprove the accuracy any further. We found two general issues.First, most core NLP systems like part-of-speech taggers and syn-tactic ... not anno-tate features of products (Update Cmd in Figure 1), generic prod-uct references (this), product mentions inside “vouches” (reviewsfrom other users), ...
... the currencies being exchanged (right). Weassess metrics of Precision, Recall, F-measure, , percentage of fullymatched posts (Ex.), and for currencies, the ... these two more effectively, leading to further overall im-provements in F-measure, , and reaching 50% exact match on posts.In the remaining ...
... our product extractor performs better at identify-ing relevant posts. Precision measures how frequently we obtain acorrect extraction when we identify a ... identify a post related to either typeof account, and recall measures how many of the gold-standardaccount-type posts we identify and classify ... F1, with gains in both precision andrecall. Note that the F-measure here captures both how often wecan surface account posts as ...
... of Naval Research under MURI grant N000140911081, by theCenter for Long-Term Cybersecurity and by gifts from Google. Wethank all the people ...
... Large Linear Classification. (2008), 1871–874.[Fleiss 1971] J. L. Fleiss. 1971. Measuring nominal scaleagreement among many raters. Psychological Bulletin 76, 5(1971), 378–382.[Franklin ... and Statistics.[Soska and Christin 2015] Kyle Soska and Nicolas Christin.2015. Measuring the longitudinal evolution of the onlineanonymous marketplace ecosystem. In 24th ...

Abstract:
... approach uses natural language processing and machine learning to automatically generate high-level information about underground forums, first identifying posts related to ...

References:
J. L. Fleiss. 1971. Measuring nominal scale agreement among many raters. Psychological Bulletin 76, 5 (1971), 378--382.
Marti Motoyama, Damon McCoy, Kirill Levchenko, Stefan Savage, and Geoffrey M. Voelker. 2011. An Analysis of Underground Forums. In Proceedings of the 2011 ACM SIGCOMM Conference on Internet Measurement Conference. ACM, 71--80.
Kyle Soska and Nicolas Christin. 2015. Measuring the longitudinal evolution of the online anonymous marketplace ecosystem. In 24th USENIX Security Symposium (USENIX Security 15). 33--48.

Keywords:
measurement

Funding Agency:
Center for Long-Term Cybersecurity

Full Text:
One tag to bind them all: measuring term abstractness in social metadataOne Tag to Bind Them All:Measuring Term Abstractnessin Social MetadataDominik Benz1,?, Christian Ko rner2,?,Andreas Hotho3, Gerd Stumme1, and ... other issues, such as under-standing the di?erent levels of tag generality (or tag abstractness), whichis essential for, among others, identifying hierarchical ... we ?rst use sev-eral large-scale ontologies and taxonomies as grounded measures of wordgenerality, including Yago, Wordnet, DMOZ and WikiTaxonomy. Then,we introduce ... introduce and apply several folksonomy-based methods to measurethe level of generality of given tags. We evaluate these methods by com-paring them ... We evaluate these methods by com-paring them with the grounded measures. . Our results suggest that thegenerality of tags in social ... of tags in social tagging systems can be approximated withsimple measures. . Our work has implications for a number of problemsrelated ... recommendation,and the acquisition of light-weight ontologies from tagging data.Keywords: tagging, generality, , measures, , emergent semantics, folk-sonomies.1 IntroductionSince the advent of participatory web ... on other issues,such as understanding the di?erent levels of tag generality (or tag abstractness),which is essential for e.g. identifying hierarchical relationships ... gap by presenting a systematic analysis ofvarious folksonomy-derived notions of term abstractness. Starting from a re-view of linguistic de?nitions of word ... abstractness, we ?rst use several large-scaleontologies and taxonomies as grounded measures of word generality, , includingYago, Wordnet, DMOZ and WikiTaxonomy. Then, we introduce and ... WikiTaxonomy. Then, we introduce and apply sev-eral folksonomy-based methods to measure the level of generality of given tags.We evaluate these methods by comparing them with ... provide empirical evidence that tag abstractness canbe approximated by simple measures. . The results of this research are relevantto all applications ... matching more speci?cterms (used usually by domain experts) to more general ones.This paper is structured as follows: At ?rst we give ... At ?rst we give an overview about relatedwork, especially regarding term abstractness and emergent semantics (Section 2).This is followed by some ... In the subsequent sectionwe give an overview of the introduced measures (section 4) and evaluate themin Section 5 with the help ...
... authors only provided exemplary proofs forthis hypothesis, lacking a well-grounded measure of tag generality. . In the follow-ing, a considerable number of approaches proposed ... a more or less explicit way methods to capture the “gener- -ality” of a tag (e.g. by investigating the centrality of ... tagging habits of individual users, Heymann [14] introduced anotherentropy-based tag generality measure in the context of tag recommendation.From a completely di?erent point ... point of view, the question of which factors deter-mine the generality or abstractness of natural language terms has been addressedby researchers coming from the areas of Linguistics ... both capturebasically independent dimensions. Allen et al. [1] identify the generality of textswith the help of a set of “reference terms” ”, whose generality level is known.They also showed up a correlation between a ... is known.They also showed up a correlation between a word’s generality and its depthin the WordNet hierarchy. In their work they ... word frequency and the comparison to a set of reference terms. . In [25],Zhang makes an attempt to distinguish the four ... makes an attempt to distinguish the four linguistic concepts fuzziness,vagueness, generality and ambiguity.3 Basic NotionsAs stated above, the main intent of ... ambiguity.3 Basic NotionsAs stated above, the main intent of a term generality measure is to allow adi?erentiation of lexical entities l1, l2, . ... c2, and hence weassume c1 to be more abstract or “general” ” than c2. LC is a set of lexical labelsfor ... ? F}| ? 1. As an example, in scienti?c contextsthe terms “article” and “paper” are often used synonymously, which would bere?ected ... aggregation of the folksonomystructure indicating which tags have occurred together. Generally
... ?U R | t1, t2 ? Tur}As we will de?ne term abstractness measures based on core ontologies, folk-sonomies and term graphs, we will commonly refer to them as term structuresS in the remainder of this paper. L(S) is a ... on the above terminology, we now formally de?ne a termabstractness measure in the following way:Definition 1. A term abstractness measure ?S based upon a term structure Sis a partial order among the lexical items L ... Rfor lexical items in order to de?ne a tag abstractness measure; ; please note thata ranking function corresponds to a partial ... (l1, l2) ??S?r(l1) > r(l2). We will denote the resulting term abstractness measure as ?Sr.4 Other possibilities are resource-based and user-based cooccurrence; we ... andcaptures a su?cient amount of information.364 D. Benz et al.4 Measures of Tag GeneralityBased on the notions de?ned above, we will ... inducing a partial order ?Fr among the set oftags.5 The measures are partially based on prior work in related areas, andbuild ... textual content of a tag itself (e.g. with linguistic methods).All measures operate solely on the folksonomy structure itself or on a ... structure itself or on a derivedterm network, making them language-independent.Frequency-based measures. . A ?rst natural intuition is that more abstracttags are ... than the tag “notebook”.We capture this intuition in the abstractness measure ?Ffreq(t) induced by theranking function freq which counts the number ... = card{(u, t′, r) ? Y : t = t′}Entropy-based measures. . Another intuition stems from information theory:Entropy measures the degree of uncertainty associated with a random variable.Considering the ... of tags as a random process, one can expect thatmore general tags show a more even distribution, because they are probablyused ... level to annotate a broad spectrum of resources.Hence, more abstract terms will have a higher entropy. This approach was alsoused by ... This approach was alsoused by Heymann [14] to capture the “generality” ” of tags in the context of tagrecommendation. We adapt ... the cooccurrence weight de?ned inSection 3). entr(x ) induces the term abstractness measure ?Fentr .Centrality Measures. . In network theory the centrality of a node v ... problem at hand, centrality can also be contemplated as a measure ofabstractness or generality, , following the intuition that more abstract terms arealso more “important”. We adopted three standard centralities (degree, close-ness, ... close-ness, betweenness). All of them can be applied to a term graph G, leaving us5 Note that all term abstractness measures based on real-value ranking functions areby construction total orders, but ... is not mandatory.One Tag to Bind Them All 365with three measures ?Gdc, ?Gbc and ?Gcc as follows: Degree centrality simply countsthe ...
... EvaluationIn order to assess the quality of the tag abstractness measures ?Ffreq , ?Fentr , ?Gdc ,?Gbc, ?Gcc and ?Fsubs introduced ... and concept hierarchies, whose hierarchical structure typi-cally contains more abstract terms like “entity” or “thing” close to the taxonomyroot, whereby more ... “entity” or “thing” close to the taxonomyroot, whereby more concrete terms are found deeper in the hierarchy. Hence, wehave chosen a ... relation connects a hyponym (more speci?c synset) toa hypernym (more general synset). A synset can have multiple hypernyms, sothat the graph ... Tagging DatasetIn order to test the performance of our proposed term
to a lower correlation. Hence, our proposed methodof “resolving” term ambiguity by constructing ?O according to Eq. 6 leads toa ... correlation. Figure 1 summarizes the correlation of each ofour analyzed measures, , grounded against each of our ground truth taxonomies.First of ... is most obvious for the DMOZ hi-erarchy, where almost all measures perform only slightly better than randomguessing. A slight exception is ... better than randomguessing. A slight exception is the entropy-based abstractness measure ?Fentropy ,which in general gives greater than 0.25 across all datasets. Another relativelyconstant impression ... across all datasets. Another relativelyconstant impression is that the centrality measures based on the tag similaritygraph (cc sim and bc sim) ... correlations are found for the WikiTaxonomy dataset, namelyby the subsumption-model-based measure subs. Apart from that, the centralitymeasures based on the tag ... previous section gave a ?rst impression of theability of each measure to predict term abstractness judgments explicitly presentin a given taxonomy. This methodology allowed ... is eithera predecessor or a successor of l2 in the term subsumption hierarchy. However,our proposed measures make further distinctions among terms between which noconnection exists within a taxonomy (e.g. the freq ... the most frequentterm t is more abstract than all other terms) ). This phenomenon can probablyalso be found when asking humans ... humans – e.g. if one would ask which of the terms “art”or “theoretical computer science” is more abstract, most people will ... are not connected by the is-a relation in(at least most) general- -purpose taxonomies.In order to extend our evaluation to these cases, ... extend our evaluation to these cases, we derived two straightfor-ward measures from a taxonomy which allow for a comparison of the ... which allow for a comparison of the abstract-ness level between terms occurring in disconnected parts of the taxonomy graph.Because this approach ... extent it makes sense to compare thegenerality of completely unrelated terms, , e.g. between “waterfall” and “chair”.370 D. Benz et al.Table ... Results from the user studyCategory Number of classi?cationsOne tag more general 41Same level 11Not comparable 154Do not know one or two ... reliable method to determinewhen humans perceive the abstractness of two terms ... as comparable or not. Forthis reason, we validated the derived measures – namely (i) the shortest path tothe taxonomy root and ... shortest path tothe taxonomy root and (ii)the number of subordinate terms – by an experimentwith human subjects.Shortest path to taxonomy root. ... most taxonomies arebuilt in a top-down fashion, whereby more abstract terms are more likely tooccur closer to the taxonomy root. Hence, ... root. Hence, a natural candidate for judging theabstractness of a term is to measure its distance to the root node. This corre-sponds to a ... corre-sponds to a ranking function sp root(l), which ranks the terms l contained ina taxonomy in ascending order by the length ... length of the shortest path between rootand l.Number of subordinate terms. . Another measure is inspired by Kammann etal. [16], who stated that “the ... embraces[. . . ]”. Given a taxonomy O and itscomprised term subsumption relation ?O, we can easily determine the numberof “sub-terms” ” by subgraph size(l) = card{(l, l′) ??O}. We are ... whether sp root(l) andsubgraph size(l) correspond to human judgments of term abstractness, we per-formed an exemplary user study with 12 participants11. ... a test set, we drew arandom sample of 100 popular terms occurring in each of our datasets; for eachterm, we selected ... each of our datasets; for eachterm, we selected 3 candidate terms, , taking into account cooccurrence informa-tion from the folksonomy DEL. ... account cooccurrence informa-tion from the folksonomy DEL. The resulting 300 term pairs were shown to theeach subject via a web interface12, ...
... size) are based on the same principle, namely that a term is moregeneral the more other terms it subsumes.Apart from that, even the simplest approach of measuring term abstractnessby the mere frequency (i.e. the number of times a ... to our gold-standard taxonomies. This has aninteresting application to the popularity/generality problem: Our results point inthe direction that popular tags are ... that popular tags are on average more abstract (or more general) )than less frequently used ones. In summary, the interpretation of ... Them All 373can be condensed in two statements: First, folksonomy-based measures of termabstractness do exhibit a partially strong correlation to well-de?ned ... of a given tag can be approxi-mated well by simple measures. .6 ConclusionsIn this paper, we performed a systematic analysis of ... ConclusionsIn this paper, we performed a systematic analysis of folksonomy-based term ab-stractness measures. . To this end, we ?rst provided a common terminology ... we ?rst provided a common terminology tosubsume the notion of term abstractness in folksonomies and core ontologies.We then contributed a methodology ... to compare the abstractness informationcontained in each of our analyzed measures to established taxonomies, namelyWordNet, Yago, DMOZ and the WikiTaxonomy. Our ... and the WikiTaxonomy. Our results suggest that cen-trality and entropy measures can di?erentiate well between abstract and concreteterms. In addition, we ... the tag cooccurence graph isa more valuable input to centrality measures compared to tag similarity graphsin order to measure abstractness. Apart from that, we also shed light on the ... popularity seems to bea fairly good indicator of the “true” generality of a given tag. These insights areuseful for all kinds ... oftag semantics. As an example, tag recommendation engines could take general- -ity information into account in order to improve their predictions, ... in folksonomies explicit.As next steps, we plan to apply our measures to identify generalists and spe-cialists in social tagging systems. A ... VENUS project funded by Land Hessen.References1. Allen, R., Wu, Y.: Generality of texts. In: Digital Libraries: People, Knowledge,and Technology. LNCS, Springer, ... D., Hotho, A., Stumme, G.: Semantic analysis of tag similar-ity measures in collaborative tagging systems. In: Proc. of the 3rd Workshop ... Lexical Database. MIT Press, Cam-bridge (1998)10. Fleiss, J., et al.: Measuring nominal scale agreement among many raters. Psycho-logical Bulletin 76(5), 378–382 ...
measures, ,we used a dataset crawled from the social bookmarking system ... by chance and to enable an e?cient computation ofthe centrality measures, , we removed all tags from the resulting graph with ... 1 summarizes thestatistics of all tagging datasets.Subsequently, we computed all term abstractness measures introduced in theprevious chapter based on DEL, COOC and SIM ... 0.65 0.7 0.75 0.8correlation(d) WikiTaxonomyFig. 1. Grounding of each introduced term abstractness measure ?S against fourground-truth taxonomies. Each bar corresponds to a term abstractness measure; ; they-axis depicts the gamma correlation as de?ned in Equation ... disambiguation techniques, we “resolve”ambiguity in the following way: The abstractness measure ?O? LC LC on thevocabulary of a core ontology O ... cycles. But despite this fact, ?O contains the complete informationwhich terms li ? LC are more abstract than other terms lj ? LC according tothe taxonomy of O. Hence we ... as a “ground truth” to judge the qualityof a given term abstractness measure ?S.We are interested how well ?O correlates to ?S; picking ... discordant pairs between?S and ?S as follows: a pair of terms l and k is called concordant w.r.t. twopartial orderings ?,??, ...
... ouruser study provided us with a well-agreed set of 41 term pairs, for which we gotreliable abstractness judgments. Denoting these pairs ... as ?manual , we can nowcheck the accuracy of the term abstractness measures introduced by sp root andsubgraph size, i.e. the percentage of ... it seems that the subgraphsize (i.e. the number of subordinate terms) ) is a more reliable predictor of humanabstractness judgments. Hence, ... O. Inorder to check how close each of our introduced term abstractness measures cor-relate, we computed the gamma correlation coe?cient [6] between the ... rela-tions (see Figure 1). Another consistent observation is that the measure based onthe tag similarity network (bc sim and cc sim) ... goal during the evaluation was to check if folksonomy-based termabstractness measures are able to make reliable judgments about the relative ab-stractness ... to make reliable judgments about the relative ab-stractness level of terms. . A ?rst consistent observation is that measures based onfrequency, entropy or centrality in the tag cooccurrence graph ... encoded in gold-standard-taxonomies.One exception is DMOZ, for which almost all measures exhibit only very weakcorrelation values. We attribute this to the ... kind of” Music and Audio. WordNet on thecontrary subsumes the term Java (among others) under taxonomically muchmore precise parents: [...] > ... 0.6 0.65 0.7 0.75 0.8correlation(d) WikiTaxonomyFig. 2. Grounding of the term abstractness measure ?S against ?Osubgraph size derivedfrom four ground-truth taxonomies. Each bar ... size derivedfrom four ground-truth taxonomies. Each bar corresponds to a term abstractness mea-sure; the y-axis depicts the gamma correlation as de?ned ... hierarchical organization scheme of DMOZ.Another consistent observation is that abstractness measures based on tagsimilarity graphs (as used e.g. by [13]) perform ... our own prior work [5], wherewe showed that distributional similarity measures (like the one used in this paperor by [13]) induce ... having the same generalitylevel. On the contrary, applying e.g. centrality measures to the “plain” tag cooc-currence graph yield better results. Hence, ... subgraph size ranking.We attribute this to the fact that both measures
S.: Comparison of generalitybased algorithm variants for automatic taxonomy generation. . In: Proc. of IIT 2009,pp. 206–210. IEEE Press, Piscataway ... Univ. Pr, Cambridge (1994)25. Zhang, Q.: Fuzziness - vagueness - generality

Abstract:
... produced by taggers for engineering light-weight ontologies. For example, existing measures of tag similarity and tag relatedness have proven crucial step ... other issues, such as understanding the different levels of tag generality (or tag abstractness), which is essential for, among others, identifying ... we first use several large-scale ontologies and taxonomies as grounded measures of word generality, , including Yago, Wordnet, DMOZ and WikiTaxonomy. Then, we introduce ... WikiTaxonomy. Then, we introduce and apply several folksonomy-based methods to measure the level of generality of given tags. We evaluate these methods by comparing them ... We evaluate these methods by comparing them with the grounded measures. . Our results suggest that the generality of tags in social tagging systems can be approximated with ... tags in social tagging systems can be approximated with simple measures. . Our work has implications for a number of problems ...

References:
Allen, R., Wu, Y.: Generality of texts. In: Digital Libraries: People, Knowledge, and Technology. LNCS, Springer, Heidelberg (2010)
Cattuto, C., Benz, D., Hotho, A., Stumme, G.: Semantic analysis of tag similarity measures in collaborative tagging systems. In: Proc. of the 3rd Workshop on Ontology Learning and Population (OLP3), Patras, Greece, pp. 39-43 (July 2008)
Fleiss, J., et al.: Measuring nominal scale agreement among many raters. Psychological Bulletin 76(5), 378-382 (1971)
Henschel, A., Woon, W.L., Wächter, T., Madnick, S.: Comparison of generality based algorithm variants for automatic taxonomy generation. In: Proc. of IIT 2009, pp. 206-210. IEEE Press, Piscataway (2009)
Zhang, Q.: Fuzziness - vagueness - generality - ambiguity. Journal of Pragmatics 29(1), 13-31 (1998).

Keywords:
measures
generality

Title:
One tag to bind them all: measuring term abstractness in social metadata

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CORPORATE U.S. Department of Justice, Office of the Attorney General

Title:
Attorney General makes key escrow announcement

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CORPORATE US Department of Justice, Office of the Attorney General C US Department of Justice, Office of the Attorney General

Full Text:
... (2013) 12:2947–2963DOI 10.1007/s11128-013-0568-yUncertainty and certainty relations for complementaryqubit observables in terms of Tsallis’ entropiesAlexey E. RasteginReceived: 20 December 2012 / Accepted: ... evidencefor sensitivity in quantifying the complementarity.Keywords Pauli observables Quantum measurement Uncertainty principle Generalized entropy Concavity1 IntroductionThe quantum-mechanical concept of complementarity is naturally ... provide a flexible tool for expressing an uncer-tainty in quantum measurements. . In view of the existing reviews [7,8], we mention ... advantages of the entropic approach[10]. For the case of two measurements, , the inequality of Maassen and Uffink [11] iswidely used. ... theMaassen–Uffink relation can be extended to a pair of POVM measurements [13,14].Entropic inequalities of the Maassen–Uffink type have emphasized a role ... uncertainty relations for a set of anti-commutingobservables were given in terms of the Shannon entropy and the so-called collision one(R nyi’s entropy ... on the Riesz theorem, unified-entropyuncertainty relations for various pairs of measurement have been obtained in [34]. In[35], we considered entropic inequalities ... inequalities beyond the scope of Riesz’s theorem. Forsome pairs of measurements, , uncertainty relations were posed in terms
... ofthree ?-entropies. By construction, this bound is not exact in general. . In the limit? ? 1+, the right-hand side of ... real ? > 0. Sowe have obtained uncertainty relations in terms of Tsallis’ ?-entropies for arbitrarypositive values of the parameter. In ... the sum of three ?-entropies for com-plementary qubit observables. In general, , these bounds are essentially depend on atype of considered ... = 11/2, where 11 denotes the identity 2 2-matrix. Measuring each of theobservables ? x , ? y, ? z ... herewith identical. It is natural to assume that with the terms (43) the maximumtakes place, when the distribution {r } also concurs ...
... the right-hand side of (48) with ? = 1 in terms of the function f1(u) defined in (28). The functionf1(u) monotonically ... maps, the point2? = arctan ?2, ? = ?/4 will generate other points in which the inequality (46) issaturated. In all ... complementarity. With smallvalues of the parameter ?, the average ?-entropic measure seems to be more sensitive.For integer ? ? 2, the ... ? 0.909. Forsuch values of ?, therefore, the average ?-entropic measure is also enough sensitivein a relative scale. In general, , this issue deserves further investigations.6 ConclusionWe have obtained new ...
... (1927). [Reprinted. In: Wheeler, J.A., Zurek, W.H. (eds.) QuantumTheory and Measurement, , pp. 62–84. Princeton University Press, Princeton (1983)]2. Hall, M.J.W.: ... Phys. Rev. 34, 163–164 (1929)10. Deutsch, D.: Uncertainty in quantum measurements. . Phys. Rev. Lett. 50, 631–633 (1983)11. Maassen, H., Uffink, ... Phys. Rev. Lett. 50, 631–633 (1983)11. Maassen, H., Uffink, J.B.M.: Generalized entropic uncertainty relations. Phys. Rev. Lett. 60, 1103–1106 (1988)12. Kraus, ... An inequality for the sum of entropies of unbiased quantum measurements. . J. Phys. AMath. Gen. 25, L363–L364 (1992)18. S nchez, J.: ... anti-commuting observables. J. Math.Phys. 49, 062105 (2008)22. R nyi, A.: On measures of entropy and information. In: Neyman, J. (ed.) Proceedings of ... pp. 547–561. University of CaliforniaPress, Berkeley (1961)23. Tsallis, C.: Possible generalization of Boltzmann–Gibbs statistics. J. Stat. Phys. 52, 479–487 (1988)24. Bialynicki-Birula, ... 479–487 (1988)24. Bialynicki-Birula, I.: Formulation of the uncertainty relations in terms of the R nyi entropies. Phys.Rev. A 74, 052101 (2006)25. Rastegin, ...
... bounds on the sum of Tsallis’?-entropies, which quantify uncertainties in measurement of complementary qubitobservables. These observables are commonly represented by the ... quantum key distribution. From this viewpoint, some uncertainty relations ininformation-theoretical terms are extensively treated in [4,16,36]. The paper is orga-nized as ... material is given. In the considered approach, uncertain-ties of quantum measurements are quantified by means of entropies. In the following,we use ... three bases given by (9) and (10) are mutually unbiased. Measurements in theseeigenbases are used in six-state cryptographic protocols [16,36].Let us ... six-state cryptographic protocols [16,36].Let us write the probabilities corresponding to measurement of each of the observ-ables ? x , ? y, ...
... that the ? commutes with ? x and|? ? = |x ?. Measuring any of the ? y and ? z in the ... whence H?(? y |?) = H?(? z |?) = ln?(2). Measuring the ? x in the state?, we obtain outcomes 1 ... a stronger bound of state-dependent form. Intheir lower bound, the term 2 ln 2 is added by the von Neumann entropy ...
... Phys. 7, 256 (2005)34. Rastegin, A.E.: Number-phase uncertainty relations in terms of generalized entropies. Quantum Inf.Comput. 12, 0743–0762 (2012)35. Rastegin, A.E.: Notes on ... 2038–2045 (1996)123Uncertainty and certainty relations for complementary qubit observables in terms of Tsallis' entropiesAbstract1 Introduction2 Definition and notation3 Tight lower bounds ...
... or merelyr = 1 cos 2?2 . (14)Substituting the post-measurements distributions (12), (13), (14) into the right-handside of (1), we, ...
... ?2??uv[g?(u) ? g?(v)]. (32)For brevity, the result is expressed in terms of the variables u = sin 2? cos ?, v ... 2? and v = sin 2? . Of course, the term g?(u) is constantand the derivative (35) is zero for ? ... n = ??? ? 1. The principal point isthat the term ??(p) is a convex function of the parameter ?. Therefore, ... the parameter ?. Therefore, for arbitrarydistributions {p }, {q }, {r } the term (30) is concave with respect to ?. It followsfrom the ...

References:
Rastegin, A.E.: Number-phase uncertainty relations in terms of generalized entropies. Quantum Inf. Comput. 12, 0743---0762 (2012)
Heisenberg, W.: Über den anschaulichen Inhalt der quanten theoretischen Kinematik und Mechanik, Zeitschrift für Physik 43, 172---198 (1927). {Reprinted. In: Wheeler, J.A., Zurek, W.H. (eds.) Quantum Theory and Measurement, pp. 62---84. Princeton University Press, Princeton (1983)}
Deutsch, D.: Uncertainty in quantum measurements. Phys. Rev. Lett. 50, 631---633 (1983)
Maassen, H., Uffink, J.B.M.: Generalized entropic uncertainty relations. Phys. Rev. Lett. 60, 1103---1106 (1988)
Krishna, M., Parthasarathy, K.R.: An entropic uncertainty principle for quantum measurements. Sankhyă� Ser. A 64, 842851 (2002)
Ivanovic, I.D.: An inequality for the sum of entropies of unbiased quantum measurements. J. Phys. A Math. Gen. 25, L363---L364 (1992)
Rényi, A.: On measures of entropy and information. In: Neyman, J. (ed.) Proceedings of 4th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 547---561. University of California Press, Berkeley (1961)
Tsallis, C.: Possible generalization of Boltzmann---Gibbs statistics. J. Stat. Phys. 52, 479---487 (1988)
Bialynicki-Birula, I.: Formulation of the uncertainty relations in terms of the Rényi entropies. Phys. Rev. A 74, 052101 (2006)

Keywords:
Generalized entropy
Quantum measurement

Title:
Uncertainty and certainty relations for complementary qubit observables in terms of Tsallis' entropies

Abstract:
The traditional method of term correlation measurement based on mutual information was analyzed to solve the problem ... on mutual information was analyzed to solve the problem that terms had to be re-extracted after the corpus changed. Due to ... normalization weakness of the above method, a new method of term correlation measurement based on general correlation coefficient was proposed. The proposed method had been applied ... coefficient was proposed. The proposed method had been applied to term extraction when the corpus changed. Experimental results show that term extraction based on general correlation coefficient can simplify the procedure of term re-extraction when the corpus was upgraded or integrated without reducing ... corpus was upgraded or integrated without reducing the capability of term

Keywords:
mutual information, normalization, general correlation coefficient, term extraction

Title:
Correlation Measurement and Extraction of Terms Based on General Correlation Coefficient

Abstract:
... is described in this paper. Client-level log data (Web audience measurement data) is used as the data of users' Web watching ... Web watching behaviors. Maximal complete bipartite graphs are searched from term- -user graph obtained from the log data without analyzing the ...

References:
9) Murata, T., "Discovery of User Communities from Web Audience Measurement Data," in Proc. of the 2004 IEEE/WIC/ACM Int. Conf. on Web Intelligence (WI2004), pp. 673-676, 2004.

Keywords:
web audience measurement data

Title:
Discovery of user communities based on terms of web log data

Full Text:
Influence measures in ridge regression when the error terms follow an Ar(1) processComput Stat (2016) 31:879–898DOI 10.1007/s00180-015-0615-5ORIGINAL PAPERInfluence measures in ridge regression when the errorterms follow an Ar(1) processTug?ba ... contrastto other article on this subject, we consider the influence measures in ridge regres-sion with autocorrelated errors. Theoretical results are illustrated ... observations.Keywords Autocorrelation Regression diagnostics Ridge estimator Multicollinearity Generalized least squares estimator1 IntroductionWe consider the general linear regression modely = 1?0 + X?1 + u (1)B ... is thefirst-order autoregressive process,Ar(1). Under Ar(1) process, the errors are generated fromui = ?ui?1 + vi , |?| < 1 vi ... u? = Pu.The parameter vector ? for model (4) is generally estimated by generalized leastsquares estimator (GLS), ?? = (Z?′Z?)?1 Z?′y?. However, in the ... has inflated variance and is too far away from the123Influence measures in ridge regression when the error terms. ... 881true value. Therefore, alternative estimators were proposed. The ridge ... practice, one or more observations may differ from the modelwhich generated by density of the data (Weisberg 1985). These differences will ...
diagnostics methods forbiased estimators.In order to measure the influence of an observation, Walker and Birch (1988)expanded some ... (1999); Jahufer and Jianbao (2009) and zkale (2013) also stud-ied influence measures in the uncorrelated and homoscedastic linear regression modelwith correlated regressors. ... regressors. zkale and A ar S k t (2015) have considered DFBET Afor generalized least squares estimator with Ar(1) and Ar(2) errors and have ... i th fitted value, y?(k)?i , can be written in terms of elements of L(k) as y?(k)?i =?nj=1 l(k)i j y?j ... ? ?2) (A11 + 2A12x ′1 + x1A22x ′1). (9)123Influence measures in ridge regression when the error terms. ... 883Since lim??1 ? ?1 = D?1 where D?1 =???????1 ... the proof is completed. ?unionsq2.2 DFFITS for autocorrelated ridge regressionTo measure the effect of influential observations on the ARR fitted values, ... influential observations on the ARR fitted values, we haveconsidered DFFITS measure under model (4). DFFITS is one of the most popularsingle-case ... fitted value obtained by deleting the i th obser-vation. DFFITS measure has been discussed by Roy and Guria (2004) under GLSregression. ... and Guria (2004) under GLSregression. We can give the DFFITS measure under ARR asDFFITS(k)i =y?(k)?i ? y?(k)?(i)SE(z?i b?(k) )=z?i(b?(k) ? b?(k)(i))SE(z?i ... been deleted.2.3 Cook’s distance for autocorrelated ridge regressionA rather standard measure for the influence of i th observation Cook’s distance definedby ... of i th observation Cook’s distance definedby Cook (1977). This measure
... estimated ?.The influence of the i th observation can be measured by the change in the center of123884 T. S k t A ar, ... (1970), Walker and Birch (1988) used two versions ofCook’s distance measure for the detection of influential observation in uncorrelatedand homoscedastic linear ... . . . , p (12)Here D(k)i is the direct generalization of Cook’s distance and D(k)?i is based on the factthat ... domestic production (DOPROD), stock formation(STOCK) and domestic consumption (CONSUM), all measures are in billions ofFrench francs for the years 1949 through ... in Fig. 1. Figure 1 shows that the autocorrelation values123Influence measures in ridge regression when the error terms. ... 8850 2 4 6 8 10 12 14?1?0.500.51Lag Sample ... 0.2662 0.253113 0.5377 0.534314 0.2899 0.2896Initially, leverage points and influence measures
... from GLSand ARR are getting close to each other, smaller measured values are obtained whenthe ARR is used.To identify the effect ... are larger in absolutevalue. The 8th observation has the largest measured value according to ARR.Table 3 presents that the four most ... by using ARR are smaller than the GLS regression. In general, , as|?| ? 1, li , l(k)i (i ?= 1) ... are more evident at? ? ?1 than ? ? 1.123Influence measures in ridge regression when the error terms. ... 887Table 2 DFFITSi andDFFITS(k)i values for Frencheconomy dataObs. GLS ... observation. Forthe other observation, both the Cook’s distance and DFFITS measures give similarstructure.Figure 7 indicates that the values of Cook’s distance ...
... also increase but this increase is not in a significant123Influence measures in ridge regression when the error terms. ... 8890 0.5 10.350.450.55kLeverage0 0.5 10,150,350,550,65kLeverage0 0.5 10.10.30.5kLeverage0 0.5 10.250.450.6kLeverage(a)(c) ... on theleverage points and influential observations is studied throughMonteCarlo simulation.To generate correlated explanatory variables, we use the equation fromMcDonald andGalarneau (1975):xi ... 100, 500. Finally, each model specification isreplicated 1000 times by generating new error terms. . For each data set, 7th obser-vation is replaced as ... of response vec-tor is made influential after the errors are generated, , variance-covariance matrix ofthe vector y has changed. But DW ... followsAr(1) process in each trial. Since the explanatory variables are generated as cor-related and then 7th observation is made as influential, ... set, there is still multicollinearity problem. Although the 7th observation123Influence measures in ridge regression when the error terms. ... 8910 0.5 102.557k|DFFITS|0 0.5 10.40.711.3k|DFFITS|0 0.5 100.511.5k|DFFITS|0 0.5 11355,5k|DFFITS|(a) ... with Ar(1) errors which contain more than one regressor withconstant term is estimated by GLS. It is observed in Table 4 ...
... distance values at fixed sample size, degree of correlation andautocorrelation.123Influence measures in ridge regression when the error terms. ... 8930 0.5 10245kCOOK0 0.5 100.050.10.150.2kCOOK0 0.5 100.10.20.30.35kCOOK0 0.5 10123kCOOK(a)(c) ... autocorrelated error model. We assessed theeffect of the new proposed measures by using a data set with Ar(1) error and alsocompared ... set with Ar(1) error and alsocompared them to the corresponding measures under the generalized least squaresregression. And finally, simulation study is done to see ... How-ever, there is not a specific pattern for other influence measures when comparedARR to the GLS. Furthermore, the autocorrelation coefficient effects ...
0466/4.55180.1047/6.50660.0587/4.76771000.0115/0.82900.0065/0.44200.0093/0.84300.0053/0.52090.0075/0.86110.0044/0.58360.0060/0.88290.0038/0.63335000.0023/0.17940.0014/0.09150.0020/0.17050.0013/0.10250.0018/0.16210.0012/0.10730.0015/0.15310.0010/0.10760.50200.1757/6.20970.1353/4.66890.1772/5.86230.1398/4.35780.1843/5.68750.1478/4.18850.2072/5.64320.1594/4.06411000.0193/0.79920.0156/0.43700.0174/0.80150.0142/0.52250.0159/0.81150.0133/0.58700.0148/0.82860.0127/0.63865000.0034/0.07880.0026/0.05400.0032/0.07610.0025/0.05720.0029/0.07410.0023/0.05910.0026/0.07270.0022/0.06050.70200.1999/6.87760.1867/5.48880.1942/6.48210.1857/5.04380.1957/6.26290.1888/4.77110.2105/6.19240.1962/4.56761000.0192/0.95390.0174/0.53490.0180/0.95220.0164/0.63420.0171/0.96130.0158/0.70880.0164/0.98090.0154/0.76975000.0026/0.07880.0022/0.06070.0025/0.07700.0022/0.06360.0024/0.07590.0022/0.06550.0023/0.07550.0021/0.0671090200.2314/6.84960.2249/5.35040.2246/6.46930.2231/4.85340.2266/6.27370.2263/4.56480.2345/6.20310.2327/4.33561000.0230/1.57800.0240/0.87340.0240/1.57420.0230/1.02840.0231/1.58870.0222/1.15010.0221/1.62120.0216/1.25305000.0024/0.12100.0025/0.10250.0025/0.11970.0025/0.10610.0025/0.11940.0025/0.10880.0025/0.12020.0025/0.11160.99201.0041/4.00460.9284/2.53941.1053/3.83990.8822/2.26741.1156/3.75010.8616/2.11811.2062/3.70650.8618/1.96871000.0287/2.22630.0281/0.97180.0294/2.23860.0268/1.23110.0280/2.27440.0259/1.44310.0264/2.33690.0250/1.62715000.0032/0.35020.0031/0.29490.0031/0.34650.0031/0.30270.0031/0.34610.0031/0.31020.0031/0.35000.0031/0.3191123Influence measures in ridge regression when the error terms. ... 8976 AppendixThe difference between b?(k) and b?(k)(i) The ARR ... (1999) A simple derivation of deletion diagnostics results for the general linear model withcorrelated errors. J R Stat Soc Series B ...
0.02830.0637/0.01960.0647/0.02920.0622/0.02310.0631/0.03020.0610/0.02550.0620/0.03140.0603/0.02755000.0170/0.00300.0156/0.00250.0163/0.00290.0153/0.00260.0157/0.00290.0149/0.00260.0149/0.00280.0143/0.0026090200.5066/0.05520.5016/0.04720.5072/0.05840.5031/0.04930.5083/0.06110.5046/0.05080.5104/0.06330.5065/0.05151000.1644/0.02540.1636/0.01760.1638/0.02620.1632/0.02060.1634/0.02700.1629/0.02280.1631/0.02800.1626/0.02455000.0384/0.00250.0380/0.00220.0382/0.00240.0379/0.00230.0380/0.00240.0378/0.00230.0378/0.00240.0376/0.00230.99200.9134/0.03130.9130/0.02400.9134/0.03390.9130/0.02570.9134/0.03590.9131/0.02690.9135/0.03740.9133/0.02721000.6679/0.01960.6679/0.01210.6679/0.02040.6679/0.01490.6679/0.02110.6679/0.01690.6679/0.02210.6679/0.01855000.2852/0.00180.2852/0.00160.2852/0.00180.2852/0.00170.2852/0.00180.2852/0.00170.2852/0.00180.2852/0.0017123Influence measures in ridge regression when the error terms.
... Stat Theory Methods A 9(12):1247–1259Walker E, Birch JB (1988) Influence measures in ridge regression. Technometrics 30(2):221–227Weisberg S (1985) Applied linear regression, ... S (1985) Applied linear regression, 2nd edn. Wiley, New Jersey123Influence measures in ridge regression when the error terms follow an Ar(1) processAbstract1 Introduction2 Influence diagnostics in autocorrelated ridge ...

Abstract:
... method for assessing the influence of single case. The influence measures in the presence of multicollinearity were discussed under the linear ... to other article on this subject, we consider the influence measures in ridge regression with autocorrelated errors. Theoretical results are illustrated ...

References:
Haslett J (1999) A simple derivation of deletion diagnostics results for the general linear model with correlated errors. J R Stat Soc Series B 61(3):603-609.
�zkale MR (2013) Influence measures in affine combination type regression. J Appl Stat 40(10):2219-2243.
Walker E, Birch JB (1988) Influence measures in ridge regression. Technometrics 30(2):221-227.

Keywords:
Generalized least squares estimator

Title:
Influence measures in ridge regression when the error terms follow an Ar(1) process

Abstract:
<p><p>Automatic Term Recognition (&lt;em&gt;ATR&lt;/em&gt;) is defined as the task of identifying domain ... (&lt;em&gt;ATR&lt;/em&gt;) is defined as the task of identifying domain specific terms from technical corpora. &lt;em&gt;Termhood-based&lt;/em&gt;approaches measure the degree that a candidate term refers to a domain specific concept. &lt;em&gt;Unithood-based&lt;/em&gt;approaches measure the attachment strength of a candidate term constituents. These methods have been evaluated using different, often incompatible ... a number of different &lt;em&gt;ATR&lt;/em&gt;methods, showing that &lt;em&gt;termhood-based&lt;/em&gt;methods achieve in general superior performance. (2) We show that the number of independent ... show that the number of independent occurrences of a candidate term is the most effective source for estimating term

References:
Evert, S., Krenn, B.: Methods for the qualitative evaluation of lexical association measures. In: ACL, Morristown, NJ, USA (2001)
Frantzi, K.T., Ananiadou, S., Mima, H.: Automatic recognition of multiword terms: the C-value/NC-value method. International Journal on Digital Libraries 3(2), 115-130 (2000)
Kageura, K., Umino, B.: Methods of automatic term recognition: a review. Terminology 3(2), 259-289 (1996)
Mcinnes, B.T.: Extending the Log Likelihood Measure to Improve Collocation Identification. Master's thesis. University of Minnesota (2004)
Nakagawa, H.: Automatic Term Recognition based on Statistics of Compound Nouns. Terminology 6(2), 195-210 (2000)
Pecina, P., Schlesinger, P.: Combining Association Measures for Collocation Extraction. In: ACL, Sydney, Australia (2006)

Keywords:
term extraction
automatic term recognition

Title:
Reviewing and Evaluating Automatic Term Recognition Techniques

Author Name:
General Manager

Full Text:
... A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbersklihyonalenasedwe present a new similarity measure between generalized fuzzy numbers. It combines the concepts of geometric distance, the ... the concepts of geometric distance, the perimeterand the height of generalized fuzzy numbers for calculating the degree of similarity between generalized fuzzy numbers. We also proveChen, 1996; Kangari & Riggs, 1989; ... the center of gravity (COG) distance to pro-pose a similarity measure between generalized fuzzy num-bers. Hsieh and Chen (1999) presented a similaritymeasure between ... a method for fuzzy riskanalysis based on the ranking of generalized trapezoidalfuzzy numbers. Chen and Chen (2003) presented a methodfor fuzzy ... (2003) presented a methodfor fuzzy risk analysis based on similarity measures of gen-eralized fuzzy numbers. Kangari and Riggs (1989) pre-analysis. Wang ... obvious thatmany facts can a?ect the result of a similarity measure, ,e.g., the shapes of fuzzy numbers, the positions of fuzzynumbers, ... of fuzzy numbers,. . ., etc. In recentyears, some similarity measures between fuzzy numbershave been presented (Chen & Chen, 2001; Chen, ... 1996;Hsieh & Chen, 1999; Lee, 1999). Chen (1996) presented asimilarity measure ... between fuzzy numbers for subjectivesome properties of the proposed similarity measure. ... . We make an experiment to use 15 sets of generalized fuzzy numbers to compare theexperimental results of the proposed method ... theexperimental results of the proposed method with the existing similarity measures. . The proposed method can overcome the drawbacks ofthe existing ... The proposed method can overcome the drawbacks ofthe existing similarity measures. . Based on the proposed similarity measure between generalized fuzzy numbers, we present a new fuzzyrisk analysis algorithm for ... where the values of the evaluating items are represented by general- -ized fuzzy numbers. The proposed method provides a useful way ... problems.? 2007 Elsevier Ltd. All rights reserved.Keywords: Fuzzy risk analysis; Generalized fuzzy numbers; Linguistic terms; ; Linguistic values; Similarity measures1. IntroductionThe task of handling risk ... & Chen, 2007;sented a method for constructing risk assessment bylinguistic terms. . Schmucker (1984) presented a methodfor fuzzy risk analysis based ... ROCUniversity of Science and Technology, Taipei County, Taiwan, ROCon similarity measures between generalized fuzzy numbers. First,www.elsevier.com/locate/eswas 36 (2009) 589–598Expert Systemswith Applicationsintegration representation distance’’. ... (2009) 589–598Expert Systemswith Applicationsintegration representation distance’’. Lee (1999) presenteda similarity measure between trapezoidal fuzzy numbers.In this paper, we present a new ... fuzzy numbers.In this paper, we present a new similarity measurebetween generalized fuzzy numbers. It combines the con-cepts of the geometric distance, ... con-cepts of the geometric distance, the perimeter and theheight of generalized fuzzy numbers for calculating thedegree of similarity between generalized fuzzy numbers.We also prove three properties of the proposed similaritymeasure. ... properties of the proposed similaritymeasure. Based on the proposed similarity measure, , wefuzzy number. If a = b = c = ... where the values of the eval-uating items are represented by generalized fuzzy numbers.The proposed method provides us a useful way for ...
... proposed similaritymeasureIn this section, we apply the proposed similarity measureof generalized fuzzy numbers to present a new fuzzy riskanalysis algorithm to ... i.e., ‘‘probability of failure’’ and‘‘severity of loss’’, where the linguistic term eRi denotesthe probability of failure of the sub-component Ai andthe ... denotesthe probability of failure of the sub-component Ai andthe linguistic term eW i denotes the severity of loss of thesub-component Ai, ... 3. Zhang (1986) uses trap-ezoidal fuzzy numbers to represent linguistic terms. . In thispaper, a 9-member linguistic term set (Zhang, 1986) is usedto represent the linguistic terms. . Each linguistic term in the9-member linguistic term set is corresponding to a general- -ized trapezoidal fuzzy number, as shown in Table 2.Assume that ... risk analysis is nowpresented as follows:Step 1: Based on the generalized fuzzy numberarithmetic operations and the fuzzy weighted meanmethod, integrate the ... 5. Structure of fuzzy riStep 2: Use the proposed similarity measure to evaluatethe degree of similarity between the fuzzy number eR ... similarity between the fuzzy number eR andTable 2A 9-member linguistic term set (Schmucker, 1984)Linguistic terms Generalized trapezoidal fuzzy numbersAbsolutely-low (0,0,0,0;1.0)Very-low (0,0,0.02,0.07;1.0)Low (0.04,0.1,0.18,0.23;1.0)Fairly-low (0.17,0.22,0.36,0.42;1.0)Medium (0.32,0.41,0.58,0.65;1.0)Fairly-high (0.58,0.63,0.80,0.86;1.0)High (0.72,0.78,0.92,0.97;1.0)Very-high ... (0.32,0.41,0.58,0.65;1.0)Fairly-high (0.58,0.63,0.80,0.86;1.0)High (0.72,0.78,0.92,0.97;1.0)Very-high (0.93,0.98,1.0,1.0;1.0)Absolutely-high (1.0,1.0,1.0,1.0;1.0)A2 Fairly-high MediumA3 Very-low Higheach linguistic term shown in Table 2. The probability offailure of the component ...
... 0:2683޼ 3:3237:In the same way, the perimeter of each linguistic term in the9-member linguistic term set can be calculated, where theresults are shown in Table ... Tables 2 and 4, the degree of sim-ilarity between the generalized trapezoidal fuzzy number eRand the linguistic term ‘‘absolutely-low’’ is evaluated asfollows:S eR; absolutely-low޼ 1? j0:1614? 0j j0:2683? ... way, we can obtain the degrees of similarity be-tween the generalized trapezoidal fuzzy number eR and theother linguistic terms, , as shown in Table 5. From Table 5,we can ... that S eR;medium 0:6538 has the largest va-lue. Therefore, the generalized trapezoidal fuzzy number eRis translated into the linguistic term ‘‘medium’’. It meansthat the probability of failure of the component ... the component A is med-Table 4The perimeter of each linguistic term in the 9-member linguistic term setLinguistic term Xi Perimeter P(Xi) of the linguistic term XiAbsolutely-low 2.0Very-low 2.091249Low 2.273048Fairly-low 2.393048Medium 2.506489Fairly-high 2.453048High 2.393048Very-high 2.091249Absolutely-high 2.0Table ... 2.0Table 5The degree of similarity between eR and each linguistic term in the 9-member linguistic term setLinguistic term Xi Degree of similarity S(eR, Xi)Absolutely-low 0.323522Very-low 0.349448Low 0.457054Fairly-low 0.592072Medium ... 6 i 6 3, we can use the pro-between the generalized trapezoidal fuzzy number eR anding similarity measures. . The proposed method can over-Fairly-high 0.6499msposed fuzzy risk analysis ...
... Tables 2 and 4, the degree of simi-larity between the generalized trapezoidal fuzzy number eRand the linguistic term ‘‘absolutely-low’’ is evaluated asfollows:S eR; absolutely-low޼ 1? j0:1845? 0j 0:2889? ... of the existing similarity measures.We also apply the proposed similarity measure to presenta new fuzzy risk analysis algorithm for dealing with ... of evaluating items are represented bygeneralized fuzzy numbers.Acknowledgementthe other linguistic terms, , respectively, as shown in Table7. From Table 7, we ... see that S eR;medium 0:6933has the largest value. Therefore, the generalized trapezoidalfuzzy number eR is translated into the linguistic term ‘‘med-ium’’. It means that the probability of failure of the ... this paper, we have presented a new similarity mea-sure between generalized ... fuzzy numbers. We have provensome properties of the proposed similarity measure. . Weuse 15 sets of generalized fuzzy numbers to compare thecalculation results of the proposed method ... 0.4026Table 7The degree of similarity between eR and each linguistic term in the 9-mamber linguistic term setLinguistic term Xi Degree of similarity S eR;X i Absolutely-low 0.3218Very-low 0.3495Low 0.4640Fairly-low 0.6113Medium ... Journal of Management Sciences, 6(1), 13–25.Chen, S. H. (1999). Ranking generalized fuzzy number with graded meanintegration. In Proceedings of the eighth ... J. & Chen, S. M. (2001). A new method to measure the similaritybetween fuzzy numbers. In Proceedings of the 10th IEEE ... S. M. (2003). Fuzzy risk analysis based on similaritymeasures of generalized fuzzy numbers. IEEE Transactions on FuzzySystems, 11(1), 45–56.Chen, S. J., ... S. M. (2007). Fuzzy risk analysis based on theranking of generalized trapezoidal fuzzy numbers. Applied Intelligence,26(1), 1–11.Chen, S. M. (1996). New ... 27(5),449–472.Hsieh, C. H. & Chen, S. H. (1999). Similarity of generalized fuzzy numberswith graded mean integration representation. In Proceedings of the ... S. H. & Chen, S. M. (2006). A new similarity measure betweengeneralized fuzzy numbers. In Proceedings of the joint 3rd internationalconference ... 589–598A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbersIntroductionBasic concepts of generalized
follows. In Section 2,we brie?y review basic concepts of generalized fuzzy num-bers (Chen, 1999) and their arithmetic operations (Chen,1985; Chen, ... 1999). In Section 3, we brie?y review some exist-ing similarity measures of fuzzy numbers from Chen (1996),Chen and Chen (2001), Hsieh ... Lee(1999). In Section 4, we present a new similarity measurebetween generalized fuzzy numbers. In Section 5, we makea comparison of the ... the calculation results of the proposedmethod with the existing similarity measures. . In Section 6,we apply the proposed similarity measure to propose a fuzzyrisk analysis algorithm to deal with fuzzy ... The conclusions are discussed in Section 7.2. Basic concepts of generalized ... fuzzy numbersIn this section, we brie?y review basic concepts of gener- ... -alized fuzzy numbers from Chen (1999). Chen (1999) repre-sented a generalized trapezoidal fuzzy number eA aseA a; b; c; d;w , ... as shown in Fig. 1. The membership functionleA of a generalized fuzzy number eA satis?es the followingconditions:(1) leA is a continuous ... leA x 0, where d 6 x 61.Fig. 1. A generalized trapezoidal fuzzy number.c2; d2;w2 , a1, b1, c1, d1, a2, b2, ... a1=d2; b1=c2; c1=b2; d1=a2; min w1;w2 : 5 3. A review of existing similarity measures between fuzzynumbersIn this section, we brie?y review some existing similaritymeasures ... 4 Generalized fuzzy numbers division B:Let eA1 and eA2 be two generalized trapezoidal fuzzynumbers, where eA1 a1; b1; c1; d1;w1 , eA2 ... c2 and d2 are real numbers.Generalized fuzzy numbers multiplication ?:eBthe generalized trapezoidal fuzzy numbers eA and eB arereviewed from Chen (1985) ... eB arereviewed from Chen (1985) and Chen (1999) as follows:(1) Generalized fuzzy numbers addition ?:eA1 ? eA2 a1; b1; c1; ... c2; d1 d2; min w1;w2 ; 1 .sume that there are two generalized trapezoidal fuzzyers eA and eB; where eA a1; a2; ... . The arithmetic operations betweenAsnumbIf w = 1, then the generalized fuzzy number eA is a normalfuzzy number, denoted as eA ... d . If a = b andc = d, then the generalized fuzzy number eA is a crispinterval. If a < b ... < b < c < d, then eA is a generalized trapezoidalwith Applications 36 (2009) 589–598hen (2001), Hsieh and Chen (1999) ... b4 , as shown inFig. 2. Chen (1996) presented a similarity measure betweenfuzzy numbers eA and eB based on the geometric distance,where ... the fuzzy numbers eC and eD.Lee (1999) presented a similarity measure between trap-ezoidal fuzzy numbers, where the degree of similarityS eA; eB ...
... eA and eB.Chen and Chen (2001) presented a similarity measurebetween generalized trapezoidal fuzzy numbers. First, theycalculate the COG points x?eA ; ... trapezoidal fuzzy numbers eA and eB; respectively.If eA is a generalized trapezoidal fuzzy number,eA a1; a2; a3; a4;weA , then the ... eB.4. A new method for calculating the degree of similaritybetween generalized fuzzy numbersIn this section, we present a new method (Wei ... (Wei & Chen,2006) to calculate the degree of similarity between general- -ized fuzzy numbers. The proposed method combines theconcepts of geometric ... combines theconcepts of geometric distance, the perimeter andthe height of generalized fuzzy numbers for calculatingthe degree of similarity between generalized fuzzy numbers.We also prove some properties of the proposed similaritymeasure. ... properties of the proposed similaritymeasure. Assume that there are two generalized trapezoidalfuzzy numbers eA and eB, where eA a1; a2; ... 6 1. Then, the degree of similarityS eA; eB between the generalized trapezoidal fuzzy numberseA and eB is calculated as follows:S eA; eB ... the value of S eA; eB , the more the similarity betweenthe generalized fuzzy numbers eA and eB.Let eA a1; a2; a3; ... a3; a4;weA and eB b1; b2; b3; b4;weB betwo generalized trapezoidal fuzzy numbers. The proposedsimilarity measure has the following properties:Property 4.1. Two generalized trapezoidal fuzzy numbers eAand eB are identical if and only ... a4;weA and eB b1; b2;b3; b4;w are two generalized trapezoidal fuzzy numbersecauseP4i 1jai ? bij P4i 1jbi ? aij, based on ...
... ;weB max weA ;weB ; (i.e., weA weB . Therefore, the generalized trapezoidalfuzzy numbers eA and eB are identical. hProperty 4.2. S eA; ... the proposed method with the results of the exist-ing similarity measures (Chen & Chen, 2001; Chen, 1996;Hsieh & Chen, 1999; Lee, ... 1 1 0.7 0.7209Set 15 0.75 1 0.95 0.9048 0.6215similarity measures. . From Table 1, we can see the draw-backs of ... 1, we can see the draw-backs of the existing similarity measures (Chen & Chen,2001; Chen, 1996; Hsieh & Chen, 1999; Lee, ... 4, we can see that eA and eB are dif-ferent generalized fuzzy numbers. However, fromTable 1, we can see that if ... 4, we can see that eA and eB are dif-ferent generalized fuzzy numbers. However, fromTable 1, we can see that if ...
A review of existing similarity measures between fuzzy numbersA new method for calculating the degree of ... numbersA new method for calculating the degree of similarity between generalized fuzzy numbersA comparison of the similarity measuresFuzzy risk analysis based ...

Abstract:
... a new method for fuzzy risk analysis based on similarity measures between generalized fuzzy numbers. First, we present a new similarity measure between generalized fuzzy numbers. It combines the concepts of geometric distance, the ... concepts of geometric distance, the perimeter and the height of generalized fuzzy numbers for calculating the degree of similarity between generalized fuzzy numbers. We also prove some properties of the proposed ... numbers. We also prove some properties of the proposed similarity measure. ... . We make an experiment to use 15 sets of generalized fuzzy numbers to compare the experimental results of the proposed ... experimental results of the proposed method with the existing similarity measures. . The proposed method can overcome the drawbacks of the ... proposed method can overcome the drawbacks of the existing similarity measures. . Based on the proposed similarity measure between generalized fuzzy numbers, we present a new fuzzy risk analysis algorithm ... where the values of the evaluating items are represented by generalized fuzzy numbers. The proposed method provides a useful way to ...

References:
Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. IEEE Transactions on Fuzzy Systems. v11 i1. 45-56.
Wei, S. H. & Chen, S. M. (2006). A new similarity measure between generalized fuzzy numbers. In Proceedings of the joint 3rd international conference on soft computing and intelligent systems and 7th international symposium on advanced intelligent systems. (pp. 315-320). Tokyo, Japan.
Chen, J. H., & Chen, S. M. (2006). A new method for ranking generalized fuzzy numbers for handling fuzzy risk analysis problems. In Proceedings of the 9th Joint Conference on Information Sciences, Kaohsiung, Taiwan, Republic of China. (pp. 1196-1199).
Chen, S. H. (1999). Ranking generalized fuzzy number with graded mean integration. In Proceedings of the eighth international fuzzy systems association world congress, Vol. 2. (pp. 899-902). Taipei, Taiwan, Republic of China.
Chen, S. J. & Chen, S. M. (2001). A new method to measure the similarity between fuzzy numbers. In Proceedings of the 10th IEEE international conference on fuzzy systems. Melbourne, Australia.
Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. Applied Intelligence. v26 i1. 1-11.
Hsieh, C. H. & Chen, S. H. (1999). Similarity of generalized fuzzy numbers with graded mean integration representation. In Proceedings of the 8th international fuzzy systems association world congress, Vol. 2 (pp. 551-555). Taipei, Taiwan, Republic of China.

Keywords:
Generalized fuzzy numbers
Linguistic terms
Similarity measures

Title:
A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers

Full Text:
An uncertainty relation in terms of generalized metric adjusted skew information and correlation measureQuantum Inf Process (2016) ... correlation measureQuantum Inf Process (2016) 15:5089–5106DOI 10.1007/s11128-016-1419-4An uncertainty relation in terms of generalized metricadjusted skew information and correlation measureYa-Jing Fan1,2 Huai-Xin Cao1 ... relation. In this paper, we prove a Schr dinger-type uncertainty relationin terms of generalized metric adjusted skew information and correlation measure byusing operator monotone functions, which reads,U (g, f )? (A)U(g, ... for Wigner–Yanase skew information and Wigner–Yanase–Dysonskew information.Keywords Uncertainty relation Generalized metric adjusted skew information Generalized metric adjusted correlation measure Wigner–Yanase skew information Wigner–Yanase–Dyson skew informationB Huai-Xin [email protected] School ... toWY skew information,Wigner–Yanase–Dyson (WYD) skewinformation, metric adjusted skew information, and generalized metric adjusted skewinformation [4–13]. Li and Cao derived a generalization of Schr dinger-type uncer-tainty relation described by WY skew information [14]. ... B]) |2,whereU?(H) =?V?(H)2 ? (V?(H) ? I?(H))2,123An uncertainty relation in terms of generalized metric… 5091I?(H) = 12Tr[(i[? 12 , H ])2] = Tr(?H2) ... classical mixing uncertainty.Therefore, U?(H) may also be regarded as a measure of quantum uncertainty. A newSchr dinger-type uncertainty relation for ? was ...
... a strongerresult than the Heisenberg uncertainty relation, Furuichi gave a generalization of theSchr dinger-type uncertainty relation by the use of the quantity ... | Corr?,?(A, B) |2, (1)1235092 Y.-J. Fan et al.where the generalized correlation measure [7] is defined byCorr?,?(X, Y ) = Tr(?X†Y ) ? ... f . One may consider I f? (A) as a generalization of WYD skew information.The authors proved the uncertainty principle in ... for themetric adjusted skew information were established in [11,12]. The generalized metricadjusted skew information I (g, f )? (A) was introduced ... (A) was introduced in [13], and a Heisenberg-typeuncertainty relation for generalized metric adjusted skew information I (g, f )? (A) orgeneralized ... information I (g, f )? (A) orgeneralized metric adjusted correlation measure was established.In this paper, we will recall some notions on ... In Sect. 3, we will give twoSchr dinger-type uncertainty relations for generalized metric adjusted skew informa-tion and establish some newuncertainty relationswith respect ... by using several canonical operator monotone functions.2 Metric adjusted correlation measure and metric adjusted skewinformationIn what follows, we use Mn(C) and ... ci Pi is the spectrum decomposition ofA.123An uncertainty relation in terms of generalized metric… 5093An operator monotone function is said to be symmetric ...
... AB) ? Tr[Am f? (L?, R?)(B)],called the metric adjusted correlation measure; ; I f? (A) = Corrs( f )? (A, A), ... 2 f (x), ?x > 0. (4)Two uncertainty relations in terms of U f? were established in [11]:U f? (A)Uf? (B) ... B ? Mn,sa(C) and ? ? Mn,+,1(C).123An uncertainty relation in terms of generalized metric… 50953 Generalized metric adjusted correlation measure ... and skewinformationIn this section, we investigate the uncertainty relation for generalized metric adjustedskew information and correlation measure. . Let g, f ? Frop satisfyingg(x) ? k (x ... (A, B) = k?i[?, A], i[?, B]??, f ,called the generalized metric adjusted (GMA) correlation measure, ,I (g, f )? (A) = Corrs(g, f )? (A, ... f )? (A) = Corrs(g, f )? (A, A),called the generalized metric adjusted (GMA) skew information.Yanagi in [13] gave some generalizations of Heisenberg uncertainty relations. Forexample, it was proved that if ... interms of the GMA skew information and the GMA correlation measure, , which is nottrivial in the casewhere AB = B ... ? f (0)(x?y)22m f (x,y), we have123An uncertainty relation in terms of generalized metric… 5097????f (0)(x ? y)22m f (x, y)????=????x + y2? ...
... Hence, we can get a new uncertainty relation withrespect to generalized metric adjusted skew information or correlation measure.Corollary 3.8 Let A, ... 12 )]= 14[Corr?(A, B) + Corr?(B, A)]123An uncertainty relation in terms of generalized metric… 5103= 12Corrs?(A, B).Therefore, (18) follows. runionsqFor A, B ? ... some existing results, we have established a Schr dinger-typeuncertainty relation in terms of generalized metric adjusted (GMA) skew informationand GMA correlation measure:U (g, f ... f )? (B),while the right-hand side contains the GMA correlation measure Corrs(g, f )? (A, B) ofthe observables A and B. ... observables A and B. As applications, we have deduced four generalized uncer-tainty relations:U?,?(A)U?,?(B) ? 4?(1 ? ?)??Corrs?,?(A, B)??2 , (23)G?,?(A)G?,?(B) ? ... inequalities contain theWYD (orWY) skew information and theWYD(or WY) correlation measure. ... . The last one is also a Schr dinger-type uncertaintyrelation in terms of GMA skew information and the GMA correlation measure.Clearly, when ... trivial even if AB = B A.123An uncertainty relation in terms of generalized metric… 5105Moreover, by mixing the lower bounds of (22) and ... K.: Schr dinger uncertainty relation, Wigner-Yanase-Dyson skew informationand metric adjusted correlation measure. . J. Math. Anal. Appl. 388, 1147–1156 (2012)7. Kosaki, H.: ...
... (2011)13. Yanagi, K., Furuichi, S., Kuriyama, K.: Uncertainty relations for generalized metric adjusted skewinformation and generalized metric adjusted correlation measure. . J. Uncertain. Anal. Appl. 1, 1–12(2013)14. Li, Q., Cao, ... Appl. 1, 1–12(2013)14. Li, Q., Cao, H.X., Du, H.K.: A generalization of Schr dinger’s uncertainty relation described by theWigner-Yanase skew information. Quantum ... S., Szameit, A.: A novel integrated quantum circuit for high-orderW-state generation and its highly precise characterization. Sci. Bull. 60, 96–100 (2015)18. ... 3459–3465 (2016)25. Rastegin, A.E.: Fine-grained uncertainty relations for several quantum measurements. . Quantum Inf.Process. 14, 783–800 (2015)26. Chen, B., Fei, S.M.: ... Chen, B., Fei, S.M.: Uncertainty relations based on mutually unbiased measurements. . Quantum Inf.Process. 14, 2227–2238 (2015)27. Petz, D.: Monotone metrics ... China Phys. Mech. Astron. 59, 630301 (2016)123An uncertainty relation in terms of generalized metric adjusted skew information and correlation measureAbstract1 Introduction2 Metric adjusted ... adjusted skew information and correlation measureAbstract1 Introduction2 Metric adjusted correlation measure and metric adjusted skew information3 Generalized metric adjusted correlation measure
... ] in [6]. Since Corrs?,?(A, B) =123An uncertainty relation in terms of generalized metric… 5099Re{Corr?,?(A, B)}, naturally, we want to know whether we ... (A)J(g, f )? (A) =?I?,?(A)J?,?(A) = U?,?(A).123An uncertainty relation in terms of generalized metric… 5101Similarly, U (g, f )? (B) = U?,?(B). Hence, ... choose appropriate function g and positive number k, l,then the generalized Heisenberg uncertainty relation can degenerate to the uncertaintyrelation with respect ... combining with (17) yields (16). runionsqCorollary 3.7 shows that the generalized uncertainty relation can degenerate tothe result with respect to WY ...

Abstract:
... In this paper, we prove a Schr&#246;dinger-type uncertainty relation in terms of generalized metric adjusted skew information and correlation measure by using operator monotone functions, which reads, $$\begin{aligned} U_\rho ^{(g,f)}(A)U_\rho ...

References:
Yanagi, K., Furuichi, S., Kuriyama, K.: Uncertainty relations for generalized metric adjusted skew information and generalized metric adjusted correlation measure. J. Uncertain. Anal. Appl. 1, 1---12 (2013)
Furuichi, S., Yanagi, K.: Schrödinger uncertainty relation, Wigner-Yanase-Dyson skew information and metric adjusted correlation measure. J. Math. Anal. Appl. 388, 1147---1156 (2012)
Li, Q., Cao, H.X., Du, H.K.: A generalization of Schrödinger's uncertainty relation described by the Wigner-Yanase skew information. Quantum Inf. Process. 14, 1513---1522 (2015)
Heilmann, R., Gräfe, M., Nolte, S., Szameit, A.: A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization. Sci. Bull. 60, 96---100 (2015)
Zhang, J., Zhang, Y., Yu, C.: Rényi entropy uncertainty relation for successive projective measurements. Quantum Inf. Process. 14, 2239---2253 (2015)
Rastegin, A.E.: Fine-grained uncertainty relations for several quantum measurements. Quantum Inf. Process. 14, 783---800 (2015)
Chen, B., Fei, S.M.: Uncertainty relations based on mutually unbiased measurements. Quantum Inf. Process. 14, 2227---2238 (2015)

Keywords:
Generalized metric adjusted correlation measure
Generalized metric adjusted skew information

Title:
An uncertainty relation in terms of generalized metric adjusted skew information and correlation measure

Full Text:
Fuzzy risk analysis using area and height based similarity measure on generalized trapezoidal fuzzy numbers and its applicationApplied Soft Computing 28 (2015) ... in reAccepted 30 NAvailable onlinKeywords:Fuzzy risk anaGeneralized trSimilarity meaLinguistic valuLinguistic term metoidal en de thirt been are r1. IntroduIn 1984, Schmucker ... 26011 Tel.: +91 9ctiallp ofChen [1] presented a new similarity measure. . For any two gener- ... -alized trapezoidal fuzzy numbers, Chen and Chen [5] introduced asimilarity measure with a concept of center of gravity (COG) dis-tance. In ... and Chen [10] presented a fuzzy risk based onranking of generalized trapezoidal fuzzy numbers. Wei and Chenhttp://dx.doi.o1568-4946/ ) curve analysis, Tang ... order of preference by ideal solution (TOPSIS) method. Using linguistic term, ,d Riggs [4] proposed a method of risk assessment int ... integratedastic risk assessment (IFSRA) approach in 2007.ese techniques, the similarity measure is very impor-lysis of fuzzy risk in a system. Chen ... 9474315945.resses: [email protected] (K. Patra),[email protected] (S.K. Mondal).433336686.[6,7] presented a new similarity measure of generalized trapezoidalfuzzy numbers to evaluate a fuzzy risk analysis using linguisticterm ... linguisticterm values. Chen and Chen [9] introduced a similarity measureusing generalized trapezoidal fuzzy number. In 2010, Xu et al. [17]also introduced ... In 2010, Xu et al. [17]also introduced a new similarity measure using COG point anda new arithmetic operator for linguistic valued ... of area and perimeter, Hejazi et al. [12]also introduced similarity measure between two generalized ... trape-zoidal fuzzy numbers.In this paper, we introduce a new similarity measure using geo-metric distance, area and height of two trapezoidal valued ... two trapezoidal valued fuzzynumbers. Some properties of the proposed similarity measure havebeen derived. Taking thirty two different sets of generalized trape-zoidal fuzzy numbers, it has been shown that the proposed ... this paper, we have proposed a newarea and height of generalized trapezmethod of similarity measure have bepared with existing techniques takingMoreover, the proposed method hassystem ... proposed method hassystem in which different parametersction a subjethe heimilarity measure onplicationidnapore 721 102, WB, Indiahod of similarity measure associating the geometric distance,fuzzy numbers. Some properties regarding the proposed ... of this method, it is com-y two different sets of generalized trapezoidal fuzzy numbers. used for calculating the fuzzy risk analysis ...
... geometrical ?gures of two trapezoidal fuzzynumbers are less. Therefore, this measurement is not truly cor-rect. Again, this table shows that our ... with the geometrical con?guration.(6) Table 2 shows that the similarity measures cannot be cal-culated for the sets (16, 24–26 and 28) ... discussions, it is concluded that our pro-posed method for similarity measure gives better results than otherexisting techniques.6. Application of our proposed ... 26 27 28 29 30 31 32 results of similarity measures via existing and proposed methods.Chen [11] Hsies and Chen [1] ... Fig. 4. Inlinguistic tetrapezoidalby the folloStep 1: of loss W?i” terms suchsub-compoStep 2: sponding geStep 3: Cand W?i of eawith the ... the values of R?i and W?i inrms and each linguistic term has been represented by a fuzzy number. Then the fuzzy ... number ofnents of the system.Then consider a set of linguistic terms and its corre-neralized trapezoidal fuzzy numbers.ompute total risk R? of ... Ci by fuzzy weighted mean methodlp of arithmetic operators of generalized
lso another generalized trapezoidal fuzzy number.hen measure the similarities of total risk R?with all givenrms in Step ... mea-ue for handling the risk analysis in a production systeminguistic terms corresponding to R?i and W?i are given inllustrate the fuzzy ... probabilityf loss in the production system. As all probabilistic val-nguistic term, , hence it may be expressed in trapezoidalers. In these ...
... ? 0.6410 ? 0.76232= 0.285.Hence according to our proposed similarity measure technique,the degree of similarity between R? and each linguistic term i.e.,linguistic valued trapezoidal fuzzy number is shown in Table 5.From ... the degree of similarity ismaximum for R? and the linguistic term “high”. Therefore, for thisTable 3Fuzzy representations of linguistic terms.Linguistic term Linguistic valued trapezoidal fuzzy numberAbsolutely low (0, 0, 0, 0 ... 0.41, 0.58, 0.65; 1.0)7; 1.0))ionaper, a new technique for similarity measure of twoalued trapezoidal fuzzy numbers has been introduced.so present some ... fuzzy numbers has been introduced.so present some properties of similarity measure in the this new technique. This method is compared with ... new technique. This method is compared with thees of similarity measure taking different thirty two setsed trapezoidal fuzzy numbers and it ... to deal with different fuzzy riskblems.h, S.H. Chen, Similarity of generalized fuzzy numbers with gradedegration representation, in: Proceedings of the 1999 ... 36 (1989) 126–131., S.M. Chen, A new method for ranking generalized fuzzy numbers fuzzy risk analysis problems, in: Proceedings of the ... Republic of China, 2006, pp.99., S.M. Chen, A new similarity measure between generalized fuzzy., in: Proceedings of the Joint 3rd International Conference on ... new approch for fuzzy risk analysis based on similarity of generalized fuzzy numbers, Expert Syst. Appl. 36 (2009) 589–598. S.M. Chen, ... Appl. 36 (2009) 589–598. S.M. Chen, A new method to measure the similarity between fuzzy, in: Proceedings of the 10th IEEE ... pp. 208–214. S.M. Chen, Fuzzy risk analysis based on similarity measures of gener- -zy numbers, IEEE Trans. Fuzzy Syst. 11 (2003) 45–56. S.M. ... S.M. Chen, Fuzzy risk analysis based on the ranking of generalized
... these two couples are not same. Hence, thismethod also cannot measure the similarity properly for above fuzzynumbers.Chen and trapinior A? =wA?wA?2?A? ... ba: = 1 section, we brie?y review some existing literaturesmilarity measure of linguistic valued trapezoidal num-is purpose, we introduce two sets ... as1 ? 144?i=1|ai ? bi|)(1)ing to this formula, the similarity measures for the sets (T?1, T?3) are given by(1 ? 14(0.2 ... above types of fuzzy numbers.Hsieh and Chen proposed a similarity measure between fuzzy numbers using “graded mean integration rep- distance”. Now ... + 1.4 + 0.76= 0.65ccording to this method, the similarity measures for the and (T?1, T?3) are11 + d(T?1, T?2)= 0.769230811 ... (Thiin Fig. cannotXu similarformulS(A?, B?)d Chen [8] presented a similarity measure between gen-pezoidal fuzzy numbers with the concept of COG. Inn, ... concept of COG. Inn, the COG (x?A?, y?A?) of a generalized trapezoidal fuzzy (a1, a2, a3, a4; wA?) is given by ... the expression (4) becomes zero. Therefore, it is not?nd the measure of similarity by this method for suchidal fuzzy numbers. Now, ... hight of the fuzzy numbers. Chen [7] presented a similarity measure between two fuzzy numbers by the formula:1 ? 144?i=1|ai ? ...
... numbers in Fig. 1(a) and (b) i.e,d S(T?1, T?3) are measured, , we get the following results:5, x?T?1= 0.35S(A?, B?)where(a4 ? ... analysis on trapezoidalection, we brie?y review the basic concept of general- -idal fuzzy numbers. For a generalized trapezoidal fuzzy (a, b, c, d; w) where a, b, ... d < x <?o review some basic operations of two general- -oidal fuzzy numbers. Assume that there are two trapezoidal fuzzy ... A? = (a1, b1, c1, d1; w1)phical representation of a generalized trapezoidal fuzzy number.K. Patra, S.K. Mondal / Applied Soft Computing ... min(w1, w2)){ ab, if a < b1, otherwisepproach of similarity measure ... based on area andapezoidal fuzzy numbersome the anomalies of similarity measure ... discussed, a new method to calculate the degree of similarityo generalized trapezoidal fuzzy numbers is presentedroposed method combines the concept of ... concept of (i) geometric) area and (iii) height of a generalized trapezoidal fuzzyn: If T? = (t1, t2, t3, t4; w) ... If T? = (t1, t2, t3, t4; w) is a generalized trapezoidaler, then the area of this fuzzy number, denoted by ... betweenlized trapezoidal fuzzy numbers.me properties of this new proposed similarity measure as follows: S(T?1, T?2) = 1 if and only if ... follows: S(T?1, T?2) = 1 if and only if two generalized trapezoidalers T?1 and T?2 are identical.(T?1, T?2) =1, then by ...
T?2) = 1 if and only if two generalized trapezoidalers T?1 and T?2 are identical.?. S(T?1, T?2) = S(T?2, ... ar(T?2) = 0, wT?1 = 1.y our de?nition, the similarity measure between T?1 andtained as(1 ? 144?i=1|t1i ? t2i|) (1 ? 12{|ar(T?1) ... Fig. 3. Graphical representation of thirty two different sets of generance of our proposed methodection, we introduce thirty two different sets ... our proposed methodection, we introduce thirty two different sets of gener- -zoidal fuzzy numbers given in Fig. 3 and for these ... our proposed method gives the best performanceng methods of similarity measure (Chen [11], Hsieh anden and Chen [8], Wei and Chen ... equal, butometrical representations for these sets it is clear thatty measures will not be equal to 1. Table 2 shows thatd ... 1. Table 2 shows thatd method gives the different similarity measures ... whichble with its geometrical representations. Also, for the8), the similarity measures are same (0.6) though theirgeometricasame drawand (31 and(2) In 19calculating ... overcome.99, Hsieh and Chen [1] introduced another method forthe similarity measure of two trapezoidal fuzzy num-s technique, the similarity measure is 1 for the sets (1,, 17, 20 and 29). ... the method of Xu et al. [17], the result ofsimilarity measure for the sets (31 and 32) are same but its ...
... A. Doostparast, S.M. Hosseini, An improved fuzzy risk analysis basedimilarity measures of generalized fuzzy numbers, Expert Syst. Appl.) 9179–9185., L.C. Chi, Predicting multilateral ... 37 (2010)1920–1927.Fuzzy risk analysis using area and height based similarity measure on generalized trapezoidal fuzzy numbers and its applic...1 Introduction2 Limitations of existing ... and its applic...1 Introduction2 Limitations of existing literatures on similarity measure between two trapezoidal fuzzy numbers3 Preliminaries of fuzzy risk analysis ... risk analysis on trapezoidal numbers4 A new approach of similarity measure based on area and height of trapezoidal fuzzy numbers5 Performance ...

Abstract:
HighlightsA new method of similarity measure of the generalized trapezoidal fuzzy numbers.Properties regarding the proposed new method.Comparison of this ... this paper, we have proposed a new method of similarity measure associating the geometric distance, area and height of generalized trapezoidal fuzzy numbers. Some properties regarding the proposed new method ... numbers. Some properties regarding the proposed new method of similarity measure have been derived. To illustrate the effectiveness of this method, ... compared with existing techniques taking thirty two different sets of generalized trapezoidal fuzzy numbers. Moreover, the proposed method has been used ...

References:
S.H. Wei, S.M. Chen, A new similarity measure between generalized fuzzy numbers., in: Proceedings of the Joint 3rd International Conference on Soft Computing and Intelligent System and 7th International Symposium on Advance Intelligent Systems, 2006, pp. 315-320.
S.H. Wei, S.M. Chen, A new approch for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers, Expert Syst. Appl., 36 (2009) 589-598.
S.J. Chen, S.M. Chen, Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers, IEEE Trans. Fuzzy Syst., 11 (2003) 45-56.
S.R. Hejazi, A. Doostparast, S.M. Hosseini, An improved fuzzy risk analysis based on new similarity measures of generalized fuzzy numbers, Expert Syst. Appl., 38 (2011) 9179-9185.
C.H. Hsieh, S.H. Chen, Similarity of generalized fuzzy numbers with graded mean integration representation, in: Proceedings of the 1999 eighth international fuzzy systems association world congress, vol. 2, 1999, pp. 551-555.
S.H. Chen, S.M. Chen, A new method for ranking generalized fuzzy numbers handling fuzzy risk analysis problems, in: Proceedings of the 9-th Joint Conference on Information Sciences, 2006, pp. 1196-1199.
S.J. Chen, S.M. Chen, A new method to measure the similarity between fuzzy numbers, in: Proceedings of the 10th IEEE International Conference on Fuzzy Systems, 2001, pp. 208-214.
S.J. Chen, S.M. Chen, Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers, Appl. Intell., 26 (2007) 1-11.

Keywords:
Linguistic terms
Similarity measure
Generalized trapezoidal fuzzy numbers

Title:
Fuzzy risk analysis using area and height based similarity measure on generalized trapezoidal fuzzy numbers and its application

Full Text:
... decision-making methods with completely unknown weights in hesitant fuzzy linguistic term settingKnowledge-Based Systems 93 (2016) 135–144Contents lists available at ScienceDirectKnowledge-Bajournal homepage: ... havin this can1eta[acamZfedcftmsBs[igh0ultiple criteria decision-making methodeights in hesitant fuzzy linguistic term. . Farhadinia?epartment of Mathematics, Quchan University of Advanced Technology, Quchan ... November 2015vailable online 19 November 2015eywords:ulti-criteria decision makingesitant fuzzy linguistic term setntropy measureimilarity measureistance measurea b s t r a c ... froup to now, there is no worterm sets (HFLTSs). Hence,entropy measures of HFLTS. IntroductionThree most important research topics in the fuzzy ... topics in the fuzzy set theory arentropy, similarity, and distance measures which have drawn the at-ention of many researchers who studied ... of entropy for fuzzy sets and their extensionsllows us to measure the degree of fuzziness, ambiguity, or the un-ertainty of a ... Shannon’sunction and furthermore they put forward an axiomatic de?nition ofntropy measure of fuzzy sets [9]. On the basis of distance betweenegrees ... that of its nearestrisp set, Kaufmann [15] suggested an entropy measure formula foruzzy sets. Yager [40] de?ned the entropy measure of a fuzzy set inerms of a lack of distinction ... Over the last decades, many researchers have developed andtudied entropy measures for extensions of fuzzy sets. Burillo andustince [3] proposed an ... extensions of fuzzy sets. Burillo andustince [3] proposed an entropy measure on interval-valued fuzzyets and intuitionstic fuzzy sets. Different from Burillo ... the concept of entropy fornterval-valued fuzzy sets. A nonprobabilistic entropy measure sug-ested by Szmidt and Kacprzyk [32] for intuitionstic fuzzy sets. ... common thatblems are associated with the predetermined weights, whereas the infor-generally incomplete. This is because of the complexity and the inherentking. ... the best of our knowledge,ing introduced the concept of entropy measure for hesitant fuzzy linguistics paper, we are going to ?ll ... ambiguities in images, Sennd Pal [31] introduced classes of entropy measures for rough sets.arhadinia [12] presented a theoretical development on the ... sets based on the intuitionistic distance andts relationship with similarity measure. ... . Farhadinia [9] investigatedhe relationship between the entropy, the similarity measure and theistance measure for hesitant fuzzy sets and interval-valued hesitantuzzy sets.In view of ... view of the relationship between the entropy and the sim-larity measure for fuzzy sets and their extensions, Zeng and Guo44] showed ... extensions, Zeng and Guo44] showed that a number of similarity measures and entropies fornterval-valued fuzzy sets can be deduced by normalized ... the basis of their axiomatic de?nitions.everal researchers showed that similarity measures and entropiesor interval-valued fuzzy sets can be transformed by each ... Li [43] discussed the relationship between the similarity andhe entropy measures of interval-valued fuzzy sets, and gave someheorems to show that ... gave someheorems to show that the similarity and the entropy measures ofnterval-valued fuzzy sets can be transformed by each other basedn ... [9] studied the systematicransformation of the entropy into the similarity measure for hesi-ant fuzzy sets and vice versa. For more study ... vice versa. For more study of the entropy and theimilarity measure, , the interested reader is referred to [18,36].There exist many ... its nature, for instance, in evaluating thespeed” of a car, terms
... ,?1,0,1, . . . , ? } be a linguis-tic term set, and suppose that H1S, H2S and H3S are three ... and H3S are three HFLTSs. Thend is called a distance measure for HFLTSs if it possesses the followingproperties:(D0) 0 ? d(H1S,H2S) ... introduced a number of distancemeasures, among them are: t• The generalized ... distance measuredg(H1S,H2S) =1NN?i=1??(1LL?l=1( |?1l? ?2l|2?)?) 1???, ? > 0;(19)• The generalized Hausdorff distance measuredgh(H1S,H2S) =1NN?i=1??( maxl=1,2,...,L( |?1l? ?2l|2?)?) 1???, ? > ... measuredgh(H1S,H2S) =1NN?i=1??( maxl=1,2,...,L( |?1l? ?2l|2?)?) 1???, ? > 0;(20)• The generalized hybrid Hamming distance measuredghh(H1S,H2S) =1NN?i=1 ???????1L ?Ll=1( |?1l??2l|2?)?+maxl=1,2,...,L( |?1l??2l|2?)?2???1?????, ? > ... a strictly monotone decreasingeal function, and d be a distance measure between HFLTSs. Then, for anyFLTS HSd(HS) =Z(2d(HS,H[0]S )) ? Z(1)Z(0) ... HSd(HS) =Z(2d(HS,H[0]S )) ? Z(1)Z(0) ? Z(1) (22)s an entropy measure for HFLTS based on the corresponding distance d.roof. It is ... 0 iff HS = H[0]S .[Proved](E3): Take into consideration the generalized distance measures dgfor HFLTSs described as (19). Thendg(HS,H[0]S ) =1NN?i=1??(1LL?l=1( |?l ? ... Theorem 3.3, different formulas can be developed to calculate thentropy measure for HFLTSs using different strictly monotone de-reasing functions Z: [0, ... following formulas stand for entropy measuresf HFLTS HS:• The entropy measure based on generalized distanceEdg (HS) = 1?2NN?i=1??(1LL?l=1( |?l|2?)?) 1???, ? > 0; (23)• ... = 1?2NN?i=1??(1LL?l=1( |?l|2?)?) 1???, ? > 0; (23)• The entropy measure based on generalized Hausdorff distanceEdgh (HS) = 1?2NN?i=1??( maxl=1,2,...,L( |?l|2?)?) 1???, ? > ... 1?2NN?i=1??( maxl=1,2,...,L( |?l|2?)?) 1???, ? > 0; (24)• The entropy measure based on generalized hybrid Hamming dis-tanceEdghh (HS) = 1?2NN?i=1 ???????1L ?Ll=1( |?l |2?)? +maxl=1,2,...,L ... ( |?1l |2? )?2???1?????, ? > 0. (25)?.2. Similarity-based entropy measures for HFLTSsIn what follows, we express the axiomatic de?nition of ... ,?1,0,1, . . . , ? } be a linguis-ic term set, and suppose that H1S, H2S and H3S are three ... H2S and H3S are three HFLTSs. Thenis called a similarity measure for HFLTSs if it possesses the followingroperties:(S0) 0 ? S(H1S,H2S) ... S(H1S,H3S).Several studies dealt with the relationship between similarityeasures and entropy measures under different fuzzy environments,uch as interval-valued intuitionistic fuzzy sets [45], ... } be a linguisticerm set, and S be a similarity measure for HFLTSs. Then,S(HS) = S(HS,HS) (26)s an entropy measure for the HFLTS HS.roof. Keeping in mind the properties of ... HFLTS HS.roof. Keeping in mind the properties of a similarity measure givenn De?nition 3.4, we show that ES satis?es the requirements ...
... 1??? 1NN?i=1??(1LL?l=1( |?1l? ?2l|2?)?) 1?????2, ? > 0; (29)• The generalized Hausdorff similarity measureSgh(H1S,H2S) = 1??? 1NN?i=1??( maxl=1,2,...,L( |?1l? ?2l|2?)?) 1?????2, ... 1NN?i=1??( maxl=1,2,...,L( |?1l? ?2l|2?)?) 1?????2, ? > 0; (30)• The generalized hybrid Hamming similarity measureSghh(H1S,H2S) = 1?????1N N?i=1???????1L ?Ll=1(|?1l??2l|2?)?+maxl=1,2,...,L(|?1l??2l|2?)?2???1?????????2, ? > 0. ... similaritymeasures given by29)–(31), we can construct a family of entropy measures for HFLTSss follows:140 B. Farhadinia / Knowledge-Based Systems 93 (2016) ... B. Farhadinia / Knowledge-Based Systems 93 (2016) 135–1441t1a?f• The entropy measure based on generalized similarityESg (HS) = 1??? 1NN?i=1??(1LL?l=1( |?l|?)?) 1?????2, ? > 0;(32)• ... = 1??? 1NN?i=1??(1LL?l=1( |?l|?)?) 1?????2, ? > 0;(32)• The entropy measure based on generalized Hausdorff similarityESgh (HS) = 1??? 1NN?i=1??( maxl=1,2,...,L( |?l|?)?) 1?????2, ? ... 1??? 1NN?i=1??( maxl=1,2,...,L( |?l|?)?) 1?????2, ? > 0;(33)• The entropy measure based on generalized hybrid Hamming sim-ilarityESghh (HS) = 1?????1N N?i=1???????1L ?Ll=1(|?l |?)? +maxl=1,2,...,L ... |?)? +maxl=1,2,...,L (|?1l |? )?2???1?????????2, ? > 0.(34)3.3. Entropies-based entropy measures for HFLTSsSuppose that the function ? : [0, 1]n ? ... introduce a set of entropy mea-sures induced by other entropy measures for HFLTSs.Theorem 3.7. Assume that ? : [0, 1]n ? ... ,?1,0,1, . . . , ? } be a linguistic term set,and Ei(i = 1, . . . ,n) be a ... 1, . . . ,n) be a set of entropy measures for HFLTSs. Then,E? (HS) = ?(E1(HS), . . . , ... = ?(E1(HS), . . . , En(HS)) (37)is an entropy measure for HFLTSs.Proof. Keeping in mind the properties of each entropy ...
... 1. Then, we proceed totilize the HFLTS entropymeasure based on generalized distance (23)sdg (HS) = 1 ?2NN?i=1??(1LL?l=1( |?l|2?)?) 1???, ? > ... wi(i = 1,2,3,4) and their ranking or-ders R[wi](i = 1,2,3,4) generated by entropy measureswith ? = 0.5.Entropy w1 w2 w3 w4R[w1] ... wi(i = 1,2,3,4) and their ranking or-ders R[wi](i = 1,2,3,4) generated by entropy measureswith ? = 1.Entropy w1 w2 w3 w4R[w1] ... wi(i = 1,2,3,4) and their ranking or-ders R[wi](i = 1,2,3,4) generated by entropy measureswith ? = 2.Entropy w1 w2 w3 w4R[w1] ... the relationship between the two ranking orders of criteriahat are generated by each pair of two different entropy measures. .[[[[[[eedless to say that choosing different values of parameter ? ... entropy mea-ures of fuzzy sets and their extensions, the entropy measures ... ofFLTSs have rarely been addressed. This motivates us to presenthree general ways to generate entropy measures for HFLTSs basedn (1) HFLTS distance measures, , (2) HFLTS similarity measures, , and3) HFLTS entropy measures. . This article provides researchers withbroad set of HFLTS entropies ... (2014). http://dx.doi.org/10.1016/j.jda.2014.10.002.[2] G. Bordogna, G. Passi, A fuzzy linguistic approach generalizing boolean informa-tion retrieval: a model and its evaluation, J. Am. ... J.A. Hong, Multi-criteria linguistic decision making based on hesitantfuzzy linguistic term sets and the aggregation of fuzzy sets, Inf. Sci. 286 ...
... Int. J. In-tell. Syst. 7 (1993) 479–492.[9] B. Farhadinia, Information measures for hesitant fuzzy sets and interval-valuedhesitant fuzzy sets, Inf. Sci. ... sets, Inf. Sci. 277 (2014)102–110.[11] B. Farhadinia, Distance and similarity measures for higher order hesitant fuzzysets, Knowledge-Based Syst. 55 (2014) 43–48.[12] ... Knowledge-Based Syst. 39 (2013) 79–84.[13] B. Farhadinia, An e?cient similarity measure for intuitionistic fuzzy sets, J. SoftComput. 18 (2014) 85–94.[14] B. ... 18 (2014) 85–94.[14] B. Farhadinia, A.I. Ban, Developing new similarity measures of generalized in-tuitionistic fuzzy numbers and generalized interval-valued fuzzy numbers fromsimilarity measures of generalized fuzzy numbers, J. Math. Comput. Modell. 57(2013) 812–825.[15] A. Kaufmann, ... Fuzzy Sets Syst. 80 (1996) 261–271.[18] X.C. Liu, Entropy, distance measure and similarity measure of fuzzy sets and theirrelations, Fuzzy Sets Syst. 52 (1992) ... Syst. 52 (1992) 305–318.[19] D.F. Li, C.T. Cheng, New similarity measure of intuitionistic fuzzy sets and appli-cation to pattern recognitions, Pattern ... Qualitative decision making with correla-tion coe?cients of hesitant fuzzy linguistic term sets, Knowledge-Based Syst. 76(2015) 127–138.22] H.C. Liao, Z.S. Xu, X.J. ... 127–138.22] H.C. Liao, Z.S. Xu, X.J. Zeng, Distance and similarity measures for hesitant fuzzylinguistic term sets and their application in multi-criteria decision making, Inf.Sci. 271 ... Liu, R.M. Rodriguez, A fuzzy envelope of hesitant fuzzy linguistic term set andits application to multi-criteria decision making, Inf. Sci. 258 ... (1972) 301–312.26] J.S. Mi, Y. Leung, W.Z. Wu, An uncertainty measure in partition-based fuzzy roughsets, Int. J. Gen. Syst. 34 (2005) ... Syst. 34 (2005) 77–90.[27] H.B. Mitchell, On the Dengfeng-Chuntian similarity measure and its applicationto pattern recognition, Pattern Recognit. Lett. 24 (2003) ... / Knowledge-Based Systems 93 (2016) 135–144[40] R.R. Yager, On the measure of fuzziness and negation, Part 1: membership in theunit interval, ... 1965, pp. 29–37.[43] W.Y. Zeng, H.X. Li, Relationship between similarity measure and entropy ofinterval-valued fuzzy sets, Fuzzy Sets Syst. 157 (2006) ... 157 (2006) 1477–1484.[44] W.Y. Zeng, P. Guo, Normalized distance, similarity measure, , inclusion measureand entropy of interval-valued fuzzy sets and their ... fuzzy sets based on dis-tance and its relationship with similarity measure, ... , Knowledge-Based Syst. 22(2009b) 449–454.[48] B. Zhu, Z.S. Xu, Consistency measures for hesitant fuzzy linguistic preference re-lations, IEEE Trans. Fuzzy Syst. ... 28–42.[30] R.M. Rodriguez, L. Martinez, F. Herrera, Hesitant fuzzy linguistic terms
D. Sen, S.K. Pal, Generalized rough sets, entropy, and image ambiguity measures, ,IEEE Trans. Syst. Man. Cybern. Part B 39 (2009) 117–128.[32] ... (2014) 575–585.[36] Z.S. Xu, An overview of distance and similarity measures of intuitionistic sets, Int.J. Uncertainty Fuzziness Knowledge-Based Syst. 16 (4) ... Fuzziness Knowledge-Based Syst. 16 (4) (2008) 529–555.[37] Z.S. Xu, Deviation measures of linguistic preference relations in group decisionmaking, Omega 33 (2005) ... decision-making methods with completely unknown weights in hesitant fuzzy linguistic term setting1 Introduction2 Hesitant fuzzy linguistic term sets (HFLTSs)3 Entropy measures for HFLTSs3.1 Distance-based entropy measures for HFLTSs3.2 Similarity-based entropy measures for HFLTSs3.3 Entropies-based entropy measures for HFLTSs4 Multiple criteria decision-making with HFLTS information4.1 Illustrative example5 ...
... and thus136 B. Farhadinia / Knowledge-Based Systems 93 (2016) 135–144lTdSwlbTas?twgstlatohwRsctiteD{ftHHShwElinguistic terms are more close to the human cognitive processes.This shows that ... the human cognitive processes.This shows that the use of linguistic terms makes experts judgmentmore reliable and informative for decision making. The ... a lin-guistic variable by using a single or simple linguistic terms. . This kindof representation of the value of a linguistic ... degree of uncertainty, the decision makers might hesitantamong several linguistic terms or need a complex linguistic term torepresent their opinions. For example, in evaluation the “speed” ofa ... expressions. Recently, mo-tivated by hesitant fuzzy sets [33] and linguistic term sets, Rodriguezet al. [30] developed the hesitant fuzzy linguistic term sets (HFLTSs)to improve the modeling and computational abilities of the ... as we know, there has been no reportconcerning the entropy measure for HFLTSs. The main objective hereis to develop a theoretical ... develop a theoretical framework that will assist researchers indesigning entropy measures of HFLTSs. This development is basedon the relationship between the ... HFLTSs. This development is basedon the relationship between the entropy measures and the similar-ity measure for HFLTSs. Furthermore, we give a theorem that allowsus to ... contribution is as follows: Section 2 reviewsthe concept of linguistic term sets and then presents the concept ofHFLTSs. Section 3 is ... the results on the transformation ofthe distance and the similarity measures to the entropy measures forHFLTSs. Moreover, the latter section describes the procedure of en-tropy ... of HFLTSs. Section 4 givesthe application of the proposed entropy measures to multi-criteriadecisionmaking with completely unknownweights in the HFLTS Set-ting. This ... This paper is concluded in Section 5.2. Hesitant fuzzy linguistic term sets (HFLTSs)In decision making problems with linguistic information, expertsusually feel ... more comfortable to express their opinions by linguisticvariables (or linguistic terms) ) because this approach is more realis-tic and it is ... Xu [38] proposed the following ?nite and totally orderediscrete linguistic term set as:= {s?|? = ??, . . . ,?1,0,1, . ... variable. For example, a set of seven (? = 3) terms S coulde given as the following:S = {s?3 = very ...
... located around0. It is necessary that the totally ordered linguistic term set S satis-es the following characteristics:1. s? < s? if ... ?;2. The negation operator is de?ned as: N(s?) = s?? .Generally, , in the aggregation procedure of linguistic labels in theotally ... the aggregation procedure of linguistic labels in theotally ordered linguistic term set S, the decision maker may dealith the aggregated result ... all the original and the re-ulted linguistic labels, the discrete term setS is extended to the con-inuous term set S = {s?|? ? [?q, q]} where q(q > ... integer. Xu [38] called s? ? S the original linguistic term, ,nd s? ? S the extended (or virtual) linguistic term. . Note that the ex-ended linguistic terms also meet the latter characteristics 1 and 2.Based on the ... followingperational laws are introduced: (see e.g. [37])For any two linguistic terms s?, s? ? S, the following conditionsolds? ? s? = ... he/she needs a complex linguistic termnstead of a single linguistic term to assess a linguistic variable. Con-inuing that work, Liao et ... ,?1,0,1, . . . , ? } be a linguistic term set. A hesitantuzzy linguistic term set (HFLTS) on X is mathematically shown inerms ofS = ... is a set of some possible values in the linguistic term setand can be characterized byS(xi) = {s?l (xi)|s?l (xi) ? ... . , L}, (8)here L denotes the number of linguistic terms in hS(xi).xample 2.2. Suppose that an expert is invited to ... be described by linguistic termsnstead of crisp values. The linguistic term set for the approximatepeed can be set up as S ... HFLEs shouldave the same length. If there are fewer linguistic terms in a HFLEhan the others, an extension of that HFLE ... same length with others. Other methods devoted to adding lin-uistic terms in a shorter HFLE can be found in [22].Throughout this ... ,?1,0,1, . . . , ? } be a linguis-ic term set, and suppose that hS = {s?l |s?l ? S, ...
... . ,?1,0,1, . . . , ? } be ainguistic term set, and suppose that H1S = {?xi,h1S(xi)?|xi ?} = {?xi, ... HShatH[?? ]S ? HS ? H[? ]S . (18). Entropy measures for HFLTSsThe main purpose of this section is to suggest ... to suggest the systematicransformation of the distance and the similarity measures into thentropy measure for HFLTSs. Achieving this goal is important to theask of ... important to theask of introducing new formulas for the entropy measure of HFLTSs.his section also discusses the need for proposing a ... a new entropy forFLTSs based on a series of entropy measures for HFLTSs.Now, let us ?rst explain the idea behind the ... us ?rst explain the idea behind the introduction of en-ropy measure for HFLTSs. One of the ?rst attempts to express the ... our best knowledge, there has been no report concerning thentropy measure for HFLTSs. However, in the same direction of Mit al. ... totally ordered linguistic138 B. Farhadinia / Knowledge-Based Systems 93 (2016) 135–144TrHEiP(term set S = {s?|? = ??, . . . ,?1,0,1, ... labels are symmetrically located around s0, wewill introduce the entropy measure for HFLTSs.Once again refer to special HFLTSs given by (9)–(12) ... Here, we are goingto de?ne a magnitude allowing us to measure the fairness degree ofa HFLTS. This idea can be concreted ... ,?1,0,1, . . . , ? } be a linguis-tic term set, and suppose that H1S and H2S are two HFLTSs. ... and H2S are two HFLTSs. Then Eis called an entropy measure for HFLTSs if it possesses the followingproperties:(E0) 0 ? E(HS) ... devoted to the main results concerning thetransformation of the information measures for HFLTSs into the en-tropy measures. .3.1. Distance-based entropy measures
... and ful-ll boundary conditions. Thus, by Theorem 3.7, we can generate theollowing entropy measures for any HFLTS HS:1. The smallest entropy:E?? (HS) = ?? ... = 1 and Ej is calculated by any HFLTS en-ropy measure proposed in this contribution asj =1nn?i=1E(hi jS), j = 1, ...
... . . . , L}]n m into account, the following lin-uistic term sets are de?ned:• Hesitant fuzzy linguistic positive ideal solution (HFLPIS)x+ ... jS,h? j) , (65)where d is an arbitrary HFLE distance measures, , and wj( j =1,2, . . . ,m) are ... for the decision makers to express their feelings byusing linguistic terms. . Assume that the company constructs theseven point linguistic scale ... the process of evaluation, the decision makers may think severallinguistic terms at the same time for a movie over a criterion. ... similar to human being’s cognition thanjust using a single linguistic term. . The linguistic expression presentedabove is appropriate to be represented ...

Abstract:
... the predetermined weights, whereas the information about criteria weights is generally incomplete. This is because of the complexity and the inherent ... there is no work having introduced the concept of entropy measure for hesitant fuzzy linguistic term sets (HFLTSs). Hence, in this paper, we are going to ... fill in this gap by developing information about how entropy measures

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Keywords:
Distance measure
Entropy measure
Hesitant fuzzy linguistic term set
Similarity measure

Title:
Multiple criteria decision-making methods with completely unknown weights in hesitant fuzzy linguistic term setting

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An improved similarity measure for generalized fuzzy numbers and its application to fuzzy risk analysisApplied Soft ... on fuzhas the higin Section 5? CorresponE-mail addhttp://dx.doi.o1568-4946/ roved similarity measure for generalized fuzzy numbers andlication to fuzzy risk analysisarzade Khorshidia,b,?, Sanaz Nikfalazarbence, ... an improved method to compute the degree of similarity between generalized trape-zoidal fuzzy numbers. The proposed similarity measure contains many features of fuzzy numbers such asgeometric distance, center ... performance of the proposed methods is comparedby the existing similarity measures using twenty different sets of generalized trapezoidal fuzzy numbers.Furthermore, the proposed method is used for fuzzy ... method is used for fuzzy risk analysis based on similarity measures. . Finally,an example is introduced to illustrate the fuzzy risk ... [3,13,19]. This comparison is obtained through eitherimilarity measures.the similarity between generalized trapezoidal fuzzy numbers has attracted many researchers to measure the degree of similar-ilarity measures have usually been used in fuzzy risk analysis. The risk ... analysis. The risk parameters of each component are evaluated subjectivelyc terms. . Then, linguistic terms are translated to fuzzy numbers. Therefore, the risk of whole ... on theters via using arithmetic operators [11]. Finally, the similarity measures are used to ?nd the risk level to which the ... the system riskented fuzzy risk analysis based on a similarity measure between fuzzy numbers using both distance and center of gravityg ... [1], a fuzzy risk analysis is performed based on similarity measures of interval-valueders. [8] used TOPSIS method in fuzzy risk analysis ... used TOPSIS method in fuzzy risk analysis based on similarity measures of generalized trapezoidal fuzzy numbers. [9] improved fuzzy risk analysis using a ... fuzzy numbers. [9] improved fuzzy risk analysis using a similarity measure for generalized fuzzy numbers. In Khorshidi et al. [22], both approachesilarity and ... processes in SPC implementation.h many studies have been developed to measure the similarity of fuzzy numbers, there are still some shortcomings ... two examples are introduced to show the most recent developed measure [14] fails to ?nd the similaritybetter similarity measure can lead to higher con?dent decision making in applications such ... This is the reason that we started a newzy similarity measure. . In other words, the purpose of this study is ... study is to propose a new formula for fuzzy similarity measure whichher capability in comparison with other previous measures. . The capability of the proposed similarity measure is investigated. The discussion on the investigation veri?es the new ... The discussion on the investigation veri?es the new formula can measure the similarity better than others.ding author.resses: [email protected] (H.A. Khorshidi), [email protected] ...
... do not contain similar fuzzy numbers. The proposed gives similarity measures less than 1 for these sets which are acceptable based ... the method of Wei and Chen [17] is unable to measure the similarity of the sets 14 and 16. There isr ... shortcoming for Hejazi et al. [9] so that no similarity measure is obtained for the sets 9, 10, 14, and 16. ... sets 9, 10, 14, and 16. This is because theirty measures cannot deal with fuzzy numbers with height zero. However, the ... fuzzy numbers with height zero. However, the proposed method can measure the similarity ofmbers in all twenty sets. It shows the ... 10 in Fig. 3, it can be seen that two generalized trapezoidal fuzzy numbers are the same with different expressions. Thed ... shows the fuzzy numbers are the same with a similarity measure of 1. However, the previous methods except Hsiehn. Hsieh and ... the previous methods except Hsiehn. Hsieh and Chen, do not measure the degree of similarity for set 10 as 1.roven in ... 3, the similarity between fuzzy numbers in set 18 is measured as zero. However, the methods presented bynd Chen [10] and ... the other hand, most of the existing methods calculate thety measure of the fuzzy numbers in set 17 as zero mistakenly. ... than the fuzzy numbers in set 18. The proposed method measures the degree of similarity for sets 17 and 18 as ... similarity.e above discussions, it is concluded that the proposed similarity measure is capable to ?nd the better results than the otherthods.ion ... than the otherthods.ion in fuzzy risk analysisection, the proposed similarity measure method for generalized trapezoidal fuzzy numbers is applied in risk assessment.ity measure can be used in various areas such as service quality ... management,13,17,21]. The value of each factor is expressed by linguistic terms. . Afterwards, These terms are translated into generalized fuzzy numbers by Table 2 [20].that there are N manufacturers ... sub-components (Aij). Each sub-component is two mentioned factors via linguistic terms as Fig. 4. Therefore, the risk of each manufacturer can ... is expressed as the following steps.r set of linguistic terms.rms Generalized trapezoidal fuzzy numberow (0.0, 0.0, 0.0, 0.0; 1)(0.0, 0.0, 0.02, ...
... manufacturer i, respectively.he proposed method (Eq. (20)) is used to measure the similarity between risk value of each manufacturer and each ... These sub-components are assessed based on risk factors by linguistic terms as shown in Table 3–5. The linguistic termsslated to fuzzy ... each manufacturer and the equivalent fuzzy number of each linguistic term is measured by theethod as Eq. (20). Therefore, it would be revealed ... S. Nikfalazar / Applied Soft Computing 52 (2017) 478–486Table 6Similarity measures for manufacturers’ risk and linguistic terms.Risk levels manufacturer C1 manufacturer ... 0.5773747. ConclusionIn this paper, a new method is proposed to measure the similarity between two generalized trapezoidal fuzzy numbers. The proposedmethod is compared by the existing ... fuzzy numbers. The proposedmethod is compared by the existing similarity measures to show the strength of the proposed method. The shortcomings ... shortcomings of the previousmethods are discussed by twenty sets of generalized trapezoidal fuzzy numbers. It is concluded that the proposed method ... is appliedin fuzzy risk analysis of manufacturing systems using linguistic terms. . The fuzzy risk analysis not only determines the risk ... L.-S. Zhu,Research[22] H.A. Khorand Negoer, but also prioritizes them in terms of their risk levels. Finally, an example is used to ... to illustrate the algorithm of the fuzzys. The proposed similarity measure is able to be employed in a wide range of ... in a wide range of practical problems under uncertainty situation.his measure can be used to solve other problems as a future ... an ef?cient way., S.-M. Chen, Fuzzy risk analysis based on measures of similarity between interval-valued fuzzy numbers, Comput. Math. Appl. 55 ... fuzzy risk analysis, Cyber. Syst. 27 (5) (1996) 449–472., Ranking generalized fuzzy number with graded mean integration, in: The Eighth International ... pp. 899–902. S.M. Chen, Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers, IEEE Trans. Fuzzy Syst. 11 (1) (2003) 45–56. ... S.M. Chen, Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers, Appl. Intell. 26 (1) (2007) 1–11., J.H. ... (2007) 1–11., J.H. Chen, Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads, Expert Syst. ... An improved fuzzy risk analysis based on a new similarity measures of generalized
... a/b =3. LiteratuIn this se[14], as theexamples. TFig. 1. A generalized trapezoidal fuzzy number.tors can in?uence on the similarity measure such as location, shape, and spread of fuzzy numbers. In ... spread of fuzzy numbers. In this paper, a new similaritytween generalized trapezoidal fuzzy numbers is proposed using geometric distance, distance of ... The perimeter ratio, which is used in the proposed similarity measure, , is introduced for the ?rst time. Somere expressed for ... introduced for the ?rst time. Somere expressed for the proposed measure. . Twenty sets of trapezoidal fuzzy numbers are used to ... better than the previous methods. In addition, the new similarity measure is appliedk analysis in a manufacturing system. of paper is ... follows. In Section 2, a brief introduction is presented on generalized trapezoidal fuzzy numbers andmatical operations. Section 3 reviews the previous ... fuzzy numbers andmatical operations. Section 3 reviews the previous similarity measures, , and brings some criticisms. Section 4 presents themilarity measure. . In Section 5, the proposed method is compared with ... expressed in Section 7.ariesction, a brief description is introduced on generalized trapezoidal fuzzy numbers and their basic arithmetic operations whichor fuzzy ... their basic arithmetic operations whichor fuzzy risk analysis. Given a generalized trapezoidal fuzzy number A? =(a1, a2, a3, a4; wA?), where ... x ? a3a3 < x < a4a4 ? x < +?(1)generalized fuzzy number A? is a normal fuzzy number and denoted ... = a2 = a3 = a4. that there are two generalized trapezoidal fuzzy numbers like A? and B? so that A? ... 1, 2, 3, 4. Some new basic arithmetic operations between generalized trapezoidal fuzzy numbers are de?ned byollows.on of two generalized trapezoidal fuzzy numbers ?: =(a1 + b1 ? a1 ... + b4 ? a4 b4; min(wA?, wB?))(2)lication of two generalized trapezoidal fuzzy numbers ?: =(a1 b1, a2 b2, ... a3 b3, a4 b4; min(wA?, wB?))(3)on of two generalized trapezoidal fuzzy numbers ?: =(a1/b4, a2/b3, a3/b2, a4/b1; min(w? , ... some previous studies in the area of fuzzy numbers’ similarity measure are reviewed. In addition, since Patra and Mondal most recent ... Patra and Mondal most recent study, show their proposed similarity measure works better than others, this measure is criticized using someherefore, the problem would be emerged, and ... and there is a need to develop a new similarity measure. .480 H.A. Khorshidi, S. Nikfalazar / Applied Soft Computing 52 ... as described in Section 2. Chen [2] de?ned the similarity measure between two fuzzynumbers based on their distance as Eq. (5).S(A?,In ... + a46(7)d Chen [4] used the concept of COG to measure the similarity between fuzzy numbers. In this approach, the COG ... ? a1) (wA? ? y?A?)2wA?(9)t, the degree of similarity is measured by Eq. (10).B?)=(1 ??4i=1|ai ? bi|4) (1 ? |x?A?? x?B?|)t (a4?a1)+(b4?b1)2 ... bi|4) (1 ? |x?A?? x?B?|)t (a4?a1)+(b4?b1)2 min(y?A?, y?B?)max(y?A?, y?B?) (10)rity measure for trapezoidal fuzzy numbers is proposed by [17] which is ...
... [18] used distance and COG concepts to present a similarity measure for trapezoidal fuzzy numbers as Eq. (13).B?)= 1 ? 12 ... whFig. 2. Graphical representation of examples of trapezoidal fuzzy numbers.milarity measure is formulated using distance, perimeters, areas, and height of fuzzy ... Mondal [14] criticized the previous studies on fuzzy numbers’ similarity measure and proposed a similarity measurece, area and height as Eq. ... |wA? ? wB?|))(19) be mentioned that in all above similarity measures, , the larger value of S(A?, B?)shows that two generalized trapezoidal fuzzye more similar. Also, S(A?, B?)= 1 denotes that ... and Mondal [14] expressed the shortcomings of the previous similarity measure. . Now, we show therawbacks of their work. In the ... of their work. In the next section, an improved similarity measure is proposed which is free from the mentionedwbacks have been ... as(T?1, T?2)and(T?1, T?3). The area of each fuzzy number andty measure for each set are calculated via using Eqs. (18) and ... 02)= 0.9e seen, the degree of similarity between(T?1, T?2)and(T?1, T?3)are measured as the same, while T?2 and T?3 are different fuzzyince ... of these three fuzzy numbers are the same, the similarity measure is just calculated based on theich is not effective.482 H.A. ... these numbers are the same with different appearances.However, the similarity measure is obtained by Eq. (19) denotes that they are not ... ? 0 + 02)= 0.95d similarity measurection, the proposed similarity measure is presented, and its properties are proven. To overcome the ... properties are proven. To overcome the above-mentioned short- improved similarity measure is proposed as Eq. (20). For the ?rst drawback, the ... between fuzzy numbers A? and B?.operties of the proposed similarity measure are introduced in the following sections: S(A?, B?)= S(B?, A?).ording ...
... 0,A? = 0, and wB? = 1. Hence, the similarity measure between fuzzy numbers A? and B? is as Eq. (20).= ... (0.1, 0.3, 0.3, 0.5; 1)set 20Fig. 3. Graphical representation of generalized ... trapezoidal fuzzy number sets.isonction, the performance of the proposed similarity measure is investigated. We introduce twenty different sets of generalized fuzzy numbers (as Fig. 3) to compare the proposed method ... 3) to compare the proposed method with the existing similarity measures which are described in Sectionts of these comparisons are shown ... as the following paragraphs.ng to, the method of Chen [2] measures the similarity of the sets 7, 8, and 11 as ... numbers in these sets are not similar. Likewise, the similarity measures for484 H.A. Khorshidi, S. Nikfalazar / Applied Soft Computing 52 ... Computing 52 (2017) 478–486Table 1Comparison results of the proposed similarity measure and the previous methods.Sets Chen [2] Hsieh and Chen [10] ...
h, S.H. Chen, Similarity of generalized fuzzy numbers with graded mean integration representation, in: the 8th ... Mondal, Fuzzy risk analysis using area and height based similarity measure on generalized trapezoidal fuzzy numbers and its application, Appl. SoftJ. 28 (2015) ... A new approach for fuzzy risk analysis based on similarity measures of generaliazed fuzzy numbers, Expert Syst. Appl. 36 (2009) 589–598.hang, ... Carolina, 1986. R.-N. Xu, Fuzzy risks analysis based on similarity measures of generalized fuzzy numbers, in: B.-Y. CAO, X.J. XIE (Eds.), Fuzzy Engineering ... Case Study, Group Decisiontiation 25 (1) (2016) 203–220.An improved similarity measure for generalized fuzzy numbers and its application to fuzzy risk analysis1 Introduction2 ...

Abstract:
Display Omitted A new method for similarity measure of the generalized trapezoidal fuzzy numbers.Proven properties of the new proposed method.Better performance ... an improved method to compute the degree of similarity between generalized trapezoidal fuzzy numbers. The proposed similarity measure contains many features of fuzzy numbers such as geometric distance, ... of the proposed methods is compared by the existing similarity measures using twenty different sets of generalized trapezoidal fuzzy numbers. Furthermore, the proposed method is used for ... method is used for fuzzy risk analysis based on similarity measures. . Finally, an example is introduced to illustrate the fuzzy ...

References:
S.J. Chen, S.M. Chen, Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers, IEEE Trans. Fuzzy Syst., 11 (2003) 45-56.
S.R. Hejazi, A. Doostparast, S.M. Hosseini, An improved fuzzy risk analysis based on a new similarity measures of generalized fuzzy numbers, Expert Syst. Appl., 38 (2011) 9179-9185.
K. Patra, S.K. Mondal, Fuzzy risk analysis using area and height based similarity measure on generalized trapezoidal fuzzy numbers and its application, Appl. Soft Comput. J., 28 (2015) 276-284.
L.-S. Zhu, R.-N. Xu, Fuzzy risks analysis based on similarity measures of generalized fuzzy numbers, in: Fuzzy Engineering and Operations Research, 60, Springer, Berlin Heidelberg, 2012, pp. 569-587.
S.-J. Chen, S.-M. Chen, Fuzzy risk analysis based on measures of similarity between interval-valued fuzzy numbers, Comput. Math. Appl., 55 (2008) 1670-1685.
S.H. Chen, Ranking generalized fuzzy number with graded mean integration, in: The Eighth International Fuzzy Systems Association World Congress, 1999, pp. 899-902.
S.J. Chen, S.M. Chen, Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers, Appl. Intell., 26 (2007) 1-11.
S.M. Chen, J.H. Chen, Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads, Expert Syst. Appl., 36 (2009) 6833-6842.
C.H. Hsieh, S.H. Chen, Similarity of generalized fuzzy numbers with graded mean integration representation, in: the 8th International Fuzzy Systems Association World Congress, 1999, pp. 551-555.
S.H. Wei, S.M. Chen, A new approach for fuzzy risk analysis based on similarity measures of generaliazed fuzzy numbers, Expert Syst. Appl., 36 (2009) 589-598.

Keywords:
Linguistic terms
Similarity measure
Generalized trapezoidal fuzzy numbers

Title:
An improved similarity measure for generalized fuzzy numbers and its application to fuzzy risk analysis