Dual Hesitant Fuzzy Sets
Bin Zhu,Zeshui Xu,Meimei Xia +2 more
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TLDR
This paper proposes dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy Sets, hesitant fuzzy set, and fuzzy multisets as special cases, and investigates the basic operations and properties of DHFSs.Abstract:Â
In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type đ fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, use a notion of nested interval to reflect their common ground, then propose an extension principle of DHFSs. Additionally, we give an example to illustrate the application of DHFSs in group forecasting.read more
Citations
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Hesitant Fuzzy Sets: State of the Art and Future Directions
Rosa M. RodrĂguez,Luis MartĂnez,Vicenç Torra,Zeshui Xu,Francisco Herrera,Francisco Herrera +5 more
TL;DR: An overview on hesitant fuzzy sets is presented with the aim of providing a clear perspective on the different concepts, tools and trends related to this extension of fuzzy sets.
Journal ArticleDOI
Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets
TL;DR: The primary goal of the study is to suggest the systematic transformation of the entropy into the similarity measure for HFSs and vice versa, and two clustering algorithms are developed under a hesitant fuzzy environment.
Journal ArticleDOI
A VIKOR-based method for hesitant fuzzy multi-criteria decision making
Huchang Liao,Zeshui Xu +1 more
TL;DR: The classical VIKOR method is extended to accommodate hesitant fuzzy circumstances, and a practical example is provided to show that the method is very effective in solving multi-criteria decision making problems with hesitant preference information.
Journal ArticleDOI
An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets
TL;DR: In this paper, a new outranking approach for multi-criteria decision-making (MCDM) problems is developed in the context of a simplified neutrosophic environment, where the truth-membership degree, indeterminacy- membership degree and falsity-Membership degree for each element are singleton subsets in 0,1.
References
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Book
Fuzzy sets
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
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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.
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The concept of a linguistic variable and its application to approximate reasoningâIIâ
TL;DR: Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.
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Fuzzy sets as a basis for a theory of possibility
TL;DR: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.