A New Similarity Measure of Interval-Valued Intuitionistic Fuzzy Sets and its Application in Commodity Recommendation

2018 ◽  
Vol 13 (1) ◽  
pp. 28
Author(s):  
Peng Luo ◽  
Yongli Li ◽  
Chong Wu
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
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 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.

scholarly journals A New Similarity Measure of Interval-Valued Intuitionistic Fuzzy Sets Considering Its Hesitancy Degree and Applications in Expert Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Chong Wu ◽  
Peng Luo ◽  
Yongli Li ◽  
Xuekun Ren
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Ideal Point ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
New Approach ◽  
Intuitionistic Fuzzy ◽  
Multicriteria Group Decision Making ◽  
Interval Valued

As an important content in fuzzy mathematics, similarity measure is used to measure the similarity degree between two fuzzy sets. Considering the existing similarity measures, most of them do not consider the hesitancy degree and some methods considering the hesitancy degree are based on the intuitionistic fuzzy sets, intuitionistic fuzzy values. It may cause some counterintuitive results in some cases. In order to make up for the drawback, we present a new approach to construct the similarity measure between two interval-valued intuitionistic fuzzy sets using the entropy measure and considering the hesitancy degree. In particular, the proposed measure was demonstrated to yield a similarity measure. Besides, some examples are given to prove the practicality and effectiveness of the new measure. We also apply the similarity measure to expert system to solve the problems on pattern recognition and the multicriteria group decision making. In these examples, we also compare it with existing methods such as other similarity measures and the ideal point method.

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