Journal ArticleDOI
On distance and correlation measures of hesitant fuzzy information
Zeshui Xu,Meimei Xia +1 more
TLDR
This paper defines the distance and correlation measures for hesitant fuzzy information and then discusses their properties in detail, finding that the results are the smallest ones among those when the values in two hesitant fuzzy elements are arranged in any permutations.Abstract:
A hesitant fuzzy set, allowing the membership of an element to be a set of several possible values, is very useful to express people's hesitancy in daily life. In this paper, we define the distance and correlation measures for hesitant fuzzy information and then discuss their properties in detail. These measures are all defined under the assumption that the values in all hesitant fuzzy elements (the fundamental units of hesitant fuzzy sets) are arranged in an increasing order and two hesitant fuzzy elements have the same length when we compare them. We can find that the results, by using the developed distance measures, are the smallest ones among those when the values in two hesitant fuzzy elements are arranged in any permutations. In addition, the derived correlation coefficients are based on different linear relationships and may have different results. © 2011 Wiley Periodicals, Inc. © 2011 Wiley Periodicals, Inc.read more
Citations
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Journal ArticleDOI
Probabilistic linguistic term sets in multi-attribute group decision making
TL;DR: An extended TOPSIS method and an aggregation-based method respectively for multi-attribute group decision making (MAGDM) with probabilistic linguistic information, and apply them to a practical case concerning strategy initiatives.
Journal ArticleDOI
Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information
Zeshui Xu,Xiaolu Zhang +1 more
TL;DR: A novel approach based on TOPSIS and the maximizing deviation method for solving MADM problems, in which the evaluation information provided by the decision maker is expressed in hesitant fuzzy elements and the information about attribute weights is incomplete is developed.
Journal ArticleDOI
Hesitant fuzzy prioritized operators and their application to multiple attribute decision making
TL;DR: This paper develops some prioritized aggregation operators for aggregating hesitant fuzzy information, and applies them to develop some models for hesitant fuzzy multiple attribute decision making (MADM) problems in which the attributes are in different priority level.
Journal ArticleDOI
Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis
TL;DR: The interval-valued HFSs and the corresponding correlation coefficient formulas are developed and demonstrated their application in clustering with intervals-valued hesitant fuzzy information through a specific numerical example.
Journal ArticleDOI
Some Hesitant Fuzzy Aggregation Operators with Their Application in Group Decision Making
Meimei Xia,Zeshui Xu,Na Chen +2 more
TL;DR: Several series of aggregation operators are proposed and two methods are proposed to determine the aggregation weight vectors based on the support degrees among aggregation arguments, so that the weight vector of decision makers are obtained more objectively.
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.
Journal ArticleDOI
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
The concept of a linguistic variable and its application to approximate reasoning—II☆
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.
Book
Fuzzy Sets and Systems: Theory and Applications
Didier Dubois,Henri Prade +1 more
TL;DR: This book effectively constitutes a detailed annotated bibliography in quasitextbook style of the some thousand contributions deemed by Messrs. Dubois and Prade to belong to the area of fuzzy set theory and its applications or interactions in a wide spectrum of scientific disciplines.