A dissimilarity Jensen-Shannon divergence measure for intuitionistic fuzzy sets

2018 ◽  
Vol 33 (11) ◽  
pp. 2216-2235 ◽  
Author(s):  
Rajesh Joshi ◽  
Satish Kumar

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 142 ◽  
Author(s):  
Qianli Zhou ◽  
Hongming Mo ◽  
Yong Deng

As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.



Author(s):  
Adeeba Umar ◽  
Ram Naresh Saraswat

Background: The notion of fuzzy set was introduced by Zadeh. After that, many researchers extended the concept of fuzzy sets in different ways. Atanassov introduced the concept of intuitionistic fuzzy sets as an extension of fuzzy sets. This concept is applied in many fields such as bio-informatics, image processing, decision making, feature selection, pattern recognition etc. Objectives: The prime objective of this paper is to introduce a new generalized intuitionistic fuzzy divergence measure with proof of its validity and discussions on its elegant properties. Applications of the proposed divergence measure in multi-attribute decision making and pattern recognition are also discussed with some numerical illustrations. Further, the proposed divergence measure is compared with other methods for solving MADM and pattern recognition problems which exist in the literature. Methods: Divergence measure method is used to measure the divergence between two given sets. Also, the results of the other existing measures are also given to compare with the proposed measure. Results: We see that our proposed divergence measure found much better results in comparison with the other existing methods. Conclusion: A new divergence measure for intuitionistic fuzzy sets is introduced with some of its properties. Applications of the proposed divergence measure to pattern recognition and MADM are illustrated through examples. The comparison of the proposed method with the existing methods shows the legacy of the results of the proposed method. It is concluded that the proposed divergence measure is effective for solving real world problems related to MADM and pattern recognition.





2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Priya Arora ◽  
V. P. Tomar

In the present paper, we introduce a new parametric fuzzy divergence measure on intuitionistic fuzzy sets. Some properties of the proposed measure are also being studied. In addition, the application of the intuitionistic fuzzy divergence measure in decision making and consequently choosing the best medicines and treatment for the patients has also been discussed. There are some diseases for which vaccine is not available. In that case, we have devised a method to choose the best treatment for the patients based on the results of clinical trials.



2019 ◽  
Vol 10 (3) ◽  
pp. 445-453
Author(s):  
R. Nagalingam ◽  
S. Rajaram


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