Hesitant fuzzy sets
TLDR
It is proved that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set, and it is proved also that the operations proposed are consistent with the ones of intuitionist fuzzy sets when applied to the envelope.Abstract:
Several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, Atanassov's intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets. In this paper, we propose hesitant fuzzy sets. Although from a formal point of view, they can be seen as fuzzy multisets, we will show that their interpretation differs from the two existing approaches for fuzzy multisets. Because of this, together with their definition, we also introduce some basic operations. In addition, we also study their relationship with intuitionistic fuzzy sets. We prove that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set. We prove also that the operations we propose are consistent with the ones of intuitionistic fuzzy sets when applied to the envelope of the hesitant fuzzy sets. © 2010 Wiley Periodicals, Inc.read more
Citations
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Journal ArticleDOI
Hesitant Fuzzy Linguistic Term Sets for Decision Making
TL;DR: The concept of a hesitant fuzzy linguistic term set is introduced to provide a linguistic and computational basis to increase the richness of linguistic elicitation based on the fuzzy linguistic approach and the use of context-free grammars by using comparative terms.
Journal ArticleDOI
Hesitant fuzzy information aggregation in decision making
Meimei Xia,Zeshui Xu +1 more
TL;DR: The relationship between intutionistic fuzzy set and hesitant fuzzy set is discussed, based on which some operations and aggregation operators for hesitant fuzzy elements are developed and their application in solving decision making problems is given.
Journal ArticleDOI
Distance and similarity measures for hesitant fuzzy sets
Zeshui Xu,Meimei Xia +1 more
TL;DR: A variety of distance measures for hesitant fuzzy sets are proposed, based on which the corresponding similarity measures can be obtained and can alleviate the influence of unduly large deviations on the aggregation results by assigning them low (or high) weights.
Proceedings ArticleDOI
On hesitant fuzzy sets and decision
Vicenç Torra,Yasuo Narukawa +1 more
TL;DR: The hesitant fuzzy sets as mentioned in this paper are a generalization of fuzzy sets where the membership is an interval, instead of being a single value, and they have been used in decision making.
Journal ArticleDOI
Application of decision-making techniques in supplier selection: A systematic review of literature
TL;DR: A systematic literature review on articles published from 2008 to 2012 on the application of DM techniques for supplier selection is provided by using a methodological decision analysis in four aspects including decision problems, decision makers, decision environments, and decision approaches.
References
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Intuitionistic fuzzy sets
TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
Journal ArticleDOI
Distances between intuitionistic fuzzy sets
Eulalia Szmidt,Janusz Kacprzyk +1 more
TL;DR: It is shown that all three parameters describing intuitionistic fuzzy sets should be taken into account while calculating those distances between intuitionistically fuzzy sets.
Journal ArticleDOI
Entropy for intuitionistic fuzzy sets
Eulalia Szmidt,Janusz Kacprzyk +1 more
TL;DR: It is shown that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of F ∩ F c and F ∪ F c .
Journal ArticleDOI
Some properties of fuzzy sets of type 2
Masaharu Mizumoto,Kokichi Tanaka +1 more
TL;DR: This paper investigates the algebraic structures of fuzzy grades under the operations of join ⊔, meet ⊓, and negation ┐ which are defined by using the extension principle, and shows that convex fuzzy grades form a commutative semiring and normal convex fuzzies form a distributive lattice under ⊢ and ⊡.
Journal ArticleDOI
On the theory of bags
TL;DR: The bag structure as a set-like object in which repeated elements are significant and the operation of selecting elements from a bag based upon their membership in a set is introduced.