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.
About: This article is published in Information Sciences.The article was published on 2011-10-01. It has received 294 citations till now. The article focuses on the topics: Fuzzy measure theory & Type-2 fuzzy sets and systems.
Citations
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TL;DR: The geometric Bonferroni mean (GBM) is explored considering both the BM and the geometric mean (GM) under hesitant fuzzy environment and the proposed aggregation operators to multi-criteria decision making are applied.
440 citations
TL;DR: A closeness index-based Pythagorean fuzzy QUALIFLEX method is developed to address hierarchical multicriteria decision making problems within Pythagorian fuzzy environment based on PFNs and IVPFNs and can deal effectively with the hierarchal structure of criteria.
360 citations
TL;DR: This paper develops a wide range of hesitant fuzzy power aggregation operators for hesitant fuzzy information and demonstrates several useful properties of the operators and discusses the relationships between them.
304 citations
TL;DR: The primary goal of the study is to suggest the systematic transformation of information measures (distance measure, similarity measure, entropy, inclusion measure) for PFSs and to show the efficiency of the proposed similarity measure.
Abstract: Pythagorean fuzzy set (PFS), originally proposed by Yager, is more capable than intuitionistic fuzzy set (IFS) to handle vagueness in the real world. The main purpose of this paper is to investigate the relationship between the distance measure, the similarity measure, the entropy, and the inclusion measure for PFSs. The primary goal of the study is to suggest the systematic transformation of information measures (distance measure, similarity measure, entropy, inclusion measure) for PFSs. For achieving this goal, some new formulae for information measures of PFSs are introduced. To show the efficiency of the proposed similarity measure, we apply it to pattern recognition, clustering analysis, and medical diagnosis. Some illustrative examples are given to support the findings and also demonstrate their practicality and effectiveness of similarity measure between PFSs.
272 citations
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.
227 citations
References
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Book•
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01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
52,705 citations
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.
13,376 citations
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.
12,530 citations
01 Jan 1975
8,942 citations
Book•
21 Sep 2019
TL;DR: In this chapter, the basic definitions and properties of the interval valued intuitionistic fuzzy sets (IVIFSs) will be introduced and the majority of the proofs below are analogous to the proofs from Chapter 1.
Abstract: In this chapter, the basic definitions and properties of the interval valued intuitionistic fuzzy sets (IVIFSs) will be introduced. We will omit the majority of the proofs below, which are, in general, analogous to the proofs from Chapter 1.
2,255 citations