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.

Using the Similarity Measure Between Intuitionistic Fuzzy Sets for the Application on Pattern Recognitions

2018 ◽  
pp. 972-985
Author(s):  
Lixin Fan
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Membership Degree ◽  
Intuitionistic Fuzzy ◽  
Definition Of

The measurement of uncertainty is an important topic for the theories dealing with uncertainty. The definition of similarity measure between two IFSs is one of the most interesting topics in IFSs theory. A similarity measure is defined to compare the information carried by IFSs. Many similarity measures have been proposed. A few of them come from the well-known distance measures. In this work, a new similarity measure between IFSs was proposed by the consideration of the information carried by the membership degree, the non-membership degree, and hesitancy degree in intuitionistic fuzzy sets (IFSs). To demonstrate the efficiency of the proposed similarity measure, various similarity measures between IFSs were compared with the proposed similarity measure between IFSs by numerical examples. The compared results demonstrated that the new similarity measure is reasonable and has stronger discrimination among them. Finally, the similarity measure was applied to pattern recognition and medical diagnosis. Two illustrative examples were provided to show the effectiveness of the pattern recognition and medical diagnosis.

Using the Similarity Measure between Intuitionistic Fuzzy Sets for the Application on Pattern Recognitions

2015 ◽  
Vol 9 (2) ◽  
pp. 24-36 ◽  
Author(s):  
Lixin Fan
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Membership Degree ◽  
Intuitionistic Fuzzy ◽  
Definition Of

The measurement of uncertainty is an important topic for the theories dealing with uncertainty. The definition of similarity measure between two IFSs is one of the most interesting topics in IFSs theory. A similarity measure is defined to compare the information carried by IFSs. Many similarity measures have been proposed. A few of them come from the well-known distance measures. In this work, a new similarity measure between IFSs was proposed by the consideration of the information carried by the membership degree, the non-membership degree, and hesitancy degree in intuitionistic fuzzy sets (IFSs). To demonstrate the efficiency of the proposed similarity measure, various similarity measures between IFSs were compared with the proposed similarity measure between IFSs by numerical examples. The compared results demonstrated that the new similarity measure is reasonable and has stronger discrimination among them. Finally, the similarity measure was applied to pattern recognition and medical diagnosis. Two illustrative examples were provided to show the effectiveness of the pattern recognition and medical diagnosis.

scholarly journals New Similarity Measure between Intuitionistic Fuzzy Multisets based on Tangent Function and its Application in Medical Diagnosis

2019 ◽  
Vol 8 (2S3) ◽  
pp. 161-165 ◽  
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Tangent Function

In recent years, Intuitionistic fuzzy set is very useful in decision making problems such as medical diagnosis, pattern recognition, clustering etc., which deals with vagueness and uncertainty. Similarity measure is a tool used to find the closeness of the intuitionistic fuzzy sets by considering the membership, nonmembership and hesitation function. In this paper, we propose an effective similarity measure based on tangent function for intuitionistic fuzzy multi sets in which membership, nonmembership, hesitation function occurs more than once and also we apply this measure in medical diagnosis and pattern recognition.

scholarly journals A Novel Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 441 ◽  
Author(s):  
Minxia Luo ◽  
Jingjing Liang
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Fuzzy Numbers ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems.

A New Similarity Measures of Intuitionistic Fuzzy Sets and Application to Pattern Recognitions

2011 ◽  
Vol 219-220 ◽  
pp. 160-164 ◽  
Author(s):  
Yan Bing Gong
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy

Intuitionistic fuzzy sets (IFSs), proposed by Atanassov, have gained attention from researchers for their applications in various fields. Then similarity measures between IFSs were developed. In this paper, firstly, some existing measures of similarity are reviewed. Then a new similarity measure is proposed and the relationships between some similarity measures are proved. Finally, the similarity measures of IFSs is applied to pattern recognition and the proposed similarity measures can provide a useful way for measuring IFSs more effectively.

scholarly journals Similarity Measures between Temporal Complex Intuitionistic Fuzzy Sets and Application in Pattern Recognition and Medical Diagnosis

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Mohammed M. Khalaf ◽  
Sayer Obaid Alharbi ◽  
Wathek Chammam
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Group Influence ◽  
Intuitionistic Fuzzy ◽  
Atanassov’S Intuitionistic Fuzzy Sets

This work addresses the issue of similarity measures between two temporal complex Atanassov’s intuitionistic fuzzy sets, many measures of similarity between complex Atanassov’s intuitionistic fuzzy sets. What was proposed before did not consider the abstention group influence, which may lead to counterintuitive results in some cases. A new structure of temporal complex Atanassov’s intuitionistic fuzzy sets is obtained. This set is formally generalized from a conventional Atanassov’s intuitionistic complex fuzzy sets. Here we analyze the limitations of the existing similarity measures. Then, a new similarity measure of temporal complex Atanassov’s intuitionistic fuzzy sets is proposed and several numeric examples are given to demonstrate the validity of the proposed measure. Finally, the proposed similarity measure is applied to pattern recognition and medical diagnosis.

Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets

2021 ◽  
pp. 1-17
Author(s):  
Changlin Xu ◽  
Juhong Shen
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
New Method ◽  
Fuzzy Decision Making ◽  
Multi Criteria Decision Making

 Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. Fermatean fuzzy set proposed by Senapati and Yager, which can easily process uncertain information in decision making, pattern recognition, medical diagnosis et al., is extension of intuitionistic fuzzy set and Pythagorean fuzzy set by relaxing the restraint conditions of the support for degrees and support against degrees. In this paper, we focus on the similarity measures of Fermatean fuzzy sets. The definitions of the Fermatean fuzzy sets similarity measures and its weighted similarity measures on discrete and continuous universes are given in turn. Then, the basic properties of the presented similarity measures are discussed. Afterward, a decision-making process under the Fermatean fuzzy environment based on TOPSIS method is established, and a new method based on the proposed Fermatean fuzzy sets similarity measures is designed to solve the problems of medical diagnosis. Ultimately, an interpretative multi-criteria decision making example and two medical diagnosis examples are provided to demonstrate the viability and effectiveness of the proposed method. Through comparing the different methods in the multi-criteria decision making and the medical diagnosis application, it is found that the new method is as efficient as the other methods. These results illustrate that the proposed method is practical in dealing with the decision making problems and medical diagnosis problems.

scholarly journals A p-Ideal in BCI-Algebras Based on Multipolar Intuitionistic Fuzzy Sets

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 993
Author(s):  
Jeong-Gon Lee ◽  
Mohammad Fozouni ◽  
Kul Hur ◽  
Young Bae Jun
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Finite Degree ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Ideal ◽  
The Relationship

In 2020, Kang, Song and Jun introduced the notion of multipolar intuitionistic fuzzy set with finite degree, which is a generalization of intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras. In this paper, we used this notion to study p-ideals of BCI-algebras. The notion of k-polar intuitionistic fuzzy p-ideals in BCI-algebras is introduced, and several properties were investigated. An example to illustrate the k-polar intuitionistic fuzzy p-ideal is given. The relationship between k-polar intuitionistic fuzzy ideal and k-polar intuitionistic fuzzy p-ideal is displayed. A k-polar intuitionistic fuzzy p-ideal is found to be k-polar intuitionistic fuzzy ideal, and an example to show that the converse is not true is provided. The notions of p-ideals and k-polar ( ∈ , ∈ ) -fuzzy p-ideal in BCI-algebras are used to study the characterization of k-polar intuitionistic p-ideal. The concept of normal k-polar intuitionistic fuzzy p-ideal is introduced, and its characterization is discussed. The process of eliciting normal k-polar intuitionistic fuzzy p-ideal using k-polar intuitionistic fuzzy p-ideal is provided.

scholarly journals Intuitionistic Fuzzy Planar Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Noura Alshehri ◽  
Muhammad Akram
Keyword(s):  
Graph Theory ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Planar Graphs ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Dual Graphs ◽  
Intuitionistic Fuzzy

Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. We introduce the notions of intuitionistic fuzzy multigraphs, intuitionistic fuzzy planar graphs, and intuitionistic fuzzy dual graphs and investigate some of their interesting properties. We also study isomorphism between intuitionistic fuzzy planar graphs.

Sign in / Sign up

Export Citation Format

Share Document