Relationship between similarity measure and entropy of interval valued fuzzy sets

2006 ◽  
Vol 157 (11) ◽  
pp. 1477-1484 ◽  
Author(s):  
Wenyi Zeng ◽  
Hongxing Li
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Interval Valued

Generalized Entropy and Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets With Application in Decision Making

2021 ◽  
Vol 10 (1) ◽  
pp. 64-93
Author(s):  
Pratiksha Tiwari
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Extended Family ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Optimal Point ◽  
Generalized Entropy ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Interval-valued intuitionistic fuzzy environment is appropriate for most of the practical scenarios involving uncertainty, vagueness, and insufficient information. Entropy, similarity, distance, inclusion, and cross entropy measures are a few methods used for measuring uncertainty and classifying fuzzy sets and its generalizations. Entropy of a fuzzy set describes fuzziness degree of the set and similarity measure measures similarity between two fuzzy or members of its extended family. This paper presents generalized entropy and similarity measures for interval-valued intuitionistic fuzzy sets. Further, the proposed similarity measure is compared with some existing measure of similarity with the help of an illustrative example, and a method is used to define optimal point using the existing information. Finally, entropy and similarity measures are used to identify best alternatives to solve multi-attribute decision making.

scholarly journals New Entropy-Based Similarity Measure between Interval-Valued Intuitionstic Fuzzy Sets

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 73 ◽  
Author(s):  
Saida Mohamed ◽  
Areeg Abdalla ◽  
Robert John
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
New Approach ◽  
Interval Valued

In this paper, we propose a new approach to constructing similarity measures using the entropy measure for Interval-Valued Intuitionistic Fuzzy Sets. In addition, we provide several illustrative examples to demonstrate the practicality and effectiveness of the proposed formula. Finally, we use the new proposed similarity measure to develop a new approach for solving problems of pattern recognition and multi-criteria fuzzy decision-making.

Control Algorithm of Interval-Valued Fuzzy Control

2012 ◽  
Vol 562-564 ◽  
pp. 2111-2115
Author(s):  
Wen Yi Zeng ◽  
Qian Yin
Keyword(s):  
Mathematical Model ◽  
Fuzzy Control ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Control Algorithm ◽  
Approximate Reasoning ◽  
The Mathematical Model ◽  
Interval Valued

In this paper, we use the similarity measure of interval-valued fuzzy sets to investigate approximate reasoning of interval-valued fuzzy sets, propose the mathematical model of interval-valued fuzzy control, and investigate its control algorithm.

Monotonic Similarity Measures of Interval-Valued Fuzzy Sets and Their Applications

2017 ◽  
Vol 25 (04) ◽  
pp. 515-544 ◽  
Author(s):  
Guannan Deng ◽  
Lianlian Song ◽  
Yanli Jiang ◽  
Jingchao Fu
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Inclusion Measure ◽  
Monotonicity Properties ◽  
Degree Of Similarity ◽  
Interval Valued

A similarity measure is a measure that indicates the degree of similarity between two objects. The purpose of this work is to investigate the monotonicity properties and applications of similarity measures on interval-valued fuzzy sets. Through analyzing the intuitions of similarities, three kinds of monotonic similarity measures are defined. Furthermore, their properties and relationships with entropy and inclusion measure are investigated and discussed. Finally, some applications of the proposed monotonic similarity measures, such as pattern recognition, medical recognition, and medical diagnosis are presented.

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