Journal ArticleDOI
Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship
Wenyi Zeng,Ping Guo +1 more
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TLDR
An axiomatic definition of an interval-valued fuzzy sets' inclusion measure which is different from Bustince's is introduced and six theorems are proposed showing how the similarity measure, the inclusion measure, and the entropy of interval- valued fuzzy sets can be deduced by the interval- valuation fuzzy sets’ normalized distance based on their axi automatic definitions.About:
This article is published in Information Sciences.The article was published on 2008-03-01. It has received 164 citations till now. The article focuses on the topics: Fuzzy set & Defuzzification.read more
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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.
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Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications
TL;DR: An entropy measure for interval-valued intuitionistic fuzzy sets is proposed, which generalizes three entropy measures defined independently by Szmidt, Wang and Huang, for intuitionism fuzzy sets and is applied to solve problems on pattern recognitions, multi-criteria fuzzy decision making and medical diagnosis.
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Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision-making
Zeshui Xu,Meimei Xia +1 more
TL;DR: Two multiattribute decision‐making methods are developed in which the attribute values are given in the form of hesitant fuzzy sets reflecting humans' hesitant thinking comprehensively, and it is found that three measures are interchangeable under certain conditions.
Journal ArticleDOI
A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition
Fatih Emre Boran,Diyar Akay +1 more
TL;DR: A new general type of similarity measure for IFS with two parameters is proposed along with its proofs and it is indicated that the proposed similarity measure does not provide any counter-intuitive cases.
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A note on information entropy measures for vague sets and its applications
Qian-Sheng Zhang,Sheng-Yi Jiang +1 more
TL;DR: A new nonprobabilistic entropy of a vague set is proposed by means of the intersection and union of the membership degree and nonmembership degree of the vague set.
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.
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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.
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A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory
A. De Luca,Settimo Termini +1 more
TL;DR: A functional defined on the class of generalized characteristic functions (fuzzy sets), called “entropy≓, is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets.