scholarly journals Representations of a Comparison Measure between Two Fuzzy Sets

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2008
Author(s):  
Juin-Han Chen ◽  
Hui-Chin Tang
Keyword(s):  
Fuzzy Sets ◽  
Disjoint Union ◽  
Axiomatic Definition ◽  
The Right

This paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: two disjoint union fuzzy sets, two disjoint fuzzy sets and two general fuzzy sets. Differences exist among the numbers of possible representations of a comparison measure for the three types of fuzzy sets restrictions. The value of comparison measure is constant for two disjoint union fuzzy sets. There are 49 candidate representations of a comparison measure for two disjoint fuzzy sets, of which 13 candidate representations with one or two terms are obtained. For each candidate representation, a variant of the general axiomatic definition for a comparison measure is presented. Choosing the right candidate representation for a given application, we can easily and efficiently calculate and compare a comparison measure.

scholarly journals A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yafei Song ◽  
Xiaodan Wang ◽  
Lei Lei ◽  
Aijun Xue
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Degree ◽  
Intuitionistic Fuzzy ◽  
Axiomatic Definition

As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns.

scholarly journals A New Entropy and Its Properties Based on the Improved Axiomatic Definition of Intuitionistic Fuzzy Entropy

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Dengying Jiang ◽  
Yaxiong Wang
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Entropy ◽  
Constraint Condition ◽  
Entropy Formula ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Entropy ◽  
Axiomatic Definition ◽  
Definition Of

Regarding the problem of the existing intuitionistic fuzzy entropy formulas in ordering the partial entropy, the constraint condition that is consistent with the intuitionistic facts is proposed in this paper, the axiomatic definition of entropy which fully reflects the intuition and fuzziness of intuitionistic fuzzy sets is given, and the improved intuitionistic fuzzy entropy formula is constructed according to the entropy axiomatic definition and its properties are studied. Finally, we compare the improved formula with the existing intuitionistic fuzzy entropy formulas, and the result turns out that the improved formula can solve the problem in the entropy ordering theoretically and practically.

MEASURING INCLUSION, SIMILARITY AND COMPATIBILITY BETWEEN ATANASSOV'S INTUITIONISTIC FUZZY SETS

2012 ◽  
Vol 20 (02) ◽  
pp. 261-280 ◽  
Author(s):  
BIN XIE ◽  
LI-WEN HAN ◽  
JU-SHENG MI
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Intuitionistic Fuzzy Sets ◽  
New Methods ◽  
Intuitionistic Fuzzy ◽  
Inclusion Measure ◽  
Axiomatic Definition ◽  
Definition Of ◽  
Degree Of Similarity ◽  
Atanassov’S Intuitionistic Fuzzy Sets

This paper establishes an axiomatic definition of inclusion measures between Atanassov's intuitionistic fuzzy (A-IF for short) sets. Some kinds of A-IF inclusion measures are constructed by different A-IF operators especially by A-IF implicator, and some new methods for measuring the degree of similarity between A-IF sets are proposed. Moreover, the similarity measure obtained from an A-IF inclusion measure satisfies properties of normal similarity measure. We then define a compatibility measure by a predicates logical idea and construct several functions to measure compatibility for an intuitionistic t -norm.

A Similarity Measure between Fuzzy Sets

2012 ◽  
Vol 229-231 ◽  
pp. 2663-2666
Author(s):  
Gao Zheng
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Measures ◽  
Axiomatic Definition ◽  
Computation Formula ◽  
Fuzzy Logic Theory

The similarity measure is one of the most useful fuzzy measures in fuzzy logic theory. In this paper, we propose a new similarity measure between fuzzy sets. As a preparation, we first choose an axiomatic definition for the similarity measure. Then, according to the chosen axiomatic definition, we propose a new computation formula. Finally, we give two examples to validate its performance. The results show that the new similarity measure is rational for fuzzy sets.

An Inclusion Measure of Fuzzy Sets and its Properties

2012 ◽  
Vol 229-231 ◽  
pp. 2667-2670
Author(s):  
Jing Wang ◽  
Zhong Wei Chen
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Inclusion Measure ◽  
Axiomatic Definition ◽  
Computation Formula

The inclusion measure between two fuzzy sets can promote fuzzy logic methods to play their full roles and has been widely used in numerous areas. In this paper, we propose a new inclusion measure of fuzzy sets. At first, we select an axiomatic definition included three axioms. Then, we give a computation formula under the constraint of three axioms, and discuss two properties of the new measure. At last, two examples are given to verify its performance. The results show that the proposed inclusion measure is reliable and rational for fuzzy sets.

scholarly journals A NOVEL FUZZY ENTROPY MEASURE AND ITS APPLICATION IN COVID-19 WITH FUZZY TOPSIS

2021 ◽  
Author(s):  
Razia Sharif
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Model Uncertainty ◽  
Multicriteria Decision Making ◽  
Fuzzy Topsis ◽  
Entropy Measure ◽  
Multicriteria Decision ◽  
Axiomatic Definition ◽  
Definition Of ◽  
Topsis Technique

Fuzzy sets (FSs) are an important tool to model uncertainty and vagueness. Entropy is being used to measure the fuzziness within a fuzzy set (FS). These entropies are used to find multicriteria decision-making. For measuring uncertainty with TOPSIS techniques an axiomatic definition of entropy measure for fuzzy sets is also given in this paper. The proposed entropy is provided to satisfy all the axioms. Several numerical examples are presented to compare the proposed entropy measure with existing entropies. The corresponding results show that the newly proposed entropy can be computed easily and give reliable results. Finally, the decision-making algorithm TOPSIS (Techniques of ordered preference similarity to ideal solution) is utilized to solve multicriteria decision-making problems (MCDM) related to daily life. In the current situation, COVID-19 has no proper medical treatment. We use TOPSIS technique to suggest an effective medicine for this pandemic. Numerical results and practical examples show the effectiveness and practical applicability of the proposed entropy.

An Entropy of Interval Type-2 Fuzzy Sets

2013 ◽  
Vol 321-324 ◽  
pp. 1999-2003 ◽  
Author(s):  
Gao Zheng ◽  
Shi Wei Yin
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Fuzzy Entropy ◽  
Calculation Formula ◽  
Membership Functions ◽  
Axiomatic Definition ◽  
Fuzzy Degree ◽  
Interval Type

The entropy shows the fuzzy degree of a fuzzy set (FS) and can be used in various areas. Aiming at the characteristics of the fuzzy entropy and type-2 fuzzy sets (IT2 FSs), we introduce a new entropy of IT2 FSs in this paper. At first, we select an axiomatic definition for it. Then, considering a fact that the operations of IT2 FSs depend on the upper membership functions (UMFs) and lower membership functions (LMFs), we propose a calculation formula and verify it accords with the four axioms of the selected definition. Finally, we use an example to illuminate its reasonable performance.

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