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.

Entropy Analysis on Intuitionistic Fuzzy Sets and Interval-Valued Intuitionistic Fuzzy Sets and its Applications in Mode Assessment on Open Communities

2018 ◽  
Vol 22 (1) ◽  
pp. 147-155 ◽  
Author(s):  
Hang Tian ◽  
Jiaru Li ◽  
Fangwei Zhang ◽  
Yujuan Xu ◽  
Caihong Cui ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
Generalized Entropy ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Entropy Measures ◽  
Interval Valued

This paper identifies four variables to reveal the internal mechanisms of the entropy measures on intuitionistic fuzzy sets (IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs). First, four variables are used to propose a pair of generalized entropy measures on IFSs and IVIFSs. Second, three specific entropy measures are put forward to illustrate the effectiveness of the generalized entropy measure functions. Third, a novel multiple attribute decision-making approach under an intuitionistic fuzzy environment is proposed. The superiority of the decision-making approach is that the weight values of the attributes are obtained by their related entropy measures. Finally, the performance of the proposed entropy regulations on IFSs and IVIFSs is illustrated through a mode assessment example on open communities.

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.

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 Some Similarity Measures for Interval-Valued Picture Fuzzy Sets and Their Applications in Decision Making

Information ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 369 ◽  
Author(s):  
Peide Liu ◽  
Muhammad Munir ◽  
Tahir Mahmood ◽  
Kifayat Ullah
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Picture Fuzzy Set ◽  
Picture Fuzzy Sets ◽  
Interval Valued

Similarity measures, distance measures and entropy measures are some common tools considered to be applied to some interesting real-life phenomena including pattern recognition, decision making, medical diagnosis and clustering. Further, interval-valued picture fuzzy sets (IVPFSs) are effective and useful to describe the fuzzy information. Therefore, this manuscript aims to develop some similarity measures for IVPFSs due to the significance of describing the membership grades of picture fuzzy set in terms of intervals. Several types cosine similarity measures, cotangent similarity measures, set-theoretic and grey similarity measures, four types of dice similarity measures and generalized dice similarity measures are developed. All the developed similarity measures are validated, and their properties are demonstrated. Two well-known problems, including mineral field recognition problems and multi-attribute decision making problems, are solved using the newly developed similarity measures. The superiorities of developed similarity measures over the similarity measures of picture fuzzy sets, interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets are demonstrated through a comparison and numerical examples.

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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