Two Trigonometric Intuitionistic Fuzzy Similarity Measures

2022 ◽  
Vol 14 (1) ◽  
pp. 0-0
Keyword(s):  
Image Processing ◽  
Pattern Recognition ◽  
Edge Detection ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Trigonometric Functions ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Similarity

Intuitionistic Fuzzy Sets(1986) invented by Atanassov(Atanassov, 1986) has gained the wide popularity among various researchers because of its applications in various fields such as image processing, edge detection, medical diagnosis, pattern recognition etc. One of the significant tool by which the decision can be made is Intuitionistic Fuzzy Similarity Measure. In this communication, the authors have introduced two new Intuitionistic fuzzy similarity measures based on the trigonometric functions and its validity is proved. The proposed similarity measure is applied to 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.

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.

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.

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 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.

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.

A NOVEL SIMILARITY MEASURE BETWEEN INTUITIONISTIC FUZZY SETS AND ITS APPLICATIONS

2013 ◽  
Vol 27 (07) ◽  
pp. 1350021 ◽  
Author(s):  
SHYI-MING CHEN ◽  
YONATHAN RANDYANTO
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Hausdorff Distance ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Degree Of Similarity

In this paper, we propose a novel similarity measure between intuitionistic fuzzy sets and apply it to deal with pattern recognition problems and medical diagnosis problems. First, we propose a new similarity measure between intuitionistic fuzzy values based on the medians of intervals, the Hausdorff distance, and the ratio of the uncertainty degrees of intuitionistic fuzzy values. We also prove some properties of the proposed similarity measure between intuitionistic fuzzy values. Then, based on the proposed similarity measure between intuitionistic fuzzy values, we propose a novel similarity measure between intuitionistic fuzzy sets. It can overcome the drawbacks of existing methods for measuring the degree of similarity between intuitionistic fuzzy sets. We also prove some properties of the proposed similarity measure between intuitionistic fuzzy sets. Finally, we apply the proposed similarity measure between intuitionistic fuzzy sets to deal with pattern recognition problems and medical diagnosis problems.

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 Cosine Similarity Measure between Hybrid Intuitionistic Fuzzy Sets and Its Application in Medical Diagnosis

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Donghai Liu ◽  
Xiaohong Chen ◽  
Dan Peng
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Cosine Similarity ◽  
Individual Decision ◽  
Intuitionistic Fuzzy ◽  
Cosine Similarity Measure ◽  
The Ideal

In this paper, a cosine similarity measure between hybrid intuitionistic fuzzy sets is proposed. The aim of the paper is to investigate the cosine similarity measure with hybrid intuitionistic fuzzy information and apply it to medical diagnosis. Firstly, we construct the cosine similarity measure between hybrid intuitionistic fuzzy sets, and the relevant properties are also discussed. In order to obtain a reasonable evaluation in group decision, the weight of experts under different attributes is determined by the projection of individual decision information on the ideal decision information, where the ideal decision information is the average values of each expert’s evaluation. Furthermore, we propose a decision method for medical diagnosis based on the cosine similarity measure between hybrid intuitionistic fuzzy sets, and the patient can be diagnosed with the disease according to the values of proposed cosine similarity measure. Finally, an example is given to illustrate feasibility and effectiveness of the proposed cosine similarity measure, which is also compared with the existing similarity measures.

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