Improved generalized dissimilarity measure‐based VIKOR method for Pythagorean fuzzy sets

2021 ◽  
Author(s):  
Muhammad Jabir Khan ◽  
Muhammad Irfan Ali ◽  
Poom Kumam ◽  
Wiyada Kumam ◽  
Muhammad Aslam ◽  
...  
Keyword(s):  
Fuzzy Sets ◽  
Dissimilarity Measure ◽  
Vikor Method ◽  
Pythagorean Fuzzy Sets

scholarly journals Some Operational Computation for Intuitionistic or Pythagorean Fuzzy Set Using C-Programming

2020 ◽  
pp. 123-132
Author(s):  
Jwngsar Moshahary
Keyword(s):  
Fuzzy Sets ◽  
Programming Language ◽  
Fuzzy Set ◽  
Pythagorean Fuzzy Set ◽  
Pythagorean Fuzzy Sets ◽  
C Programming Language ◽  
C Programming

Intuitionistic or pythagorean fuzzy sets are the best tools to deal with uncertainty or ambiguity to solve diverse disciplines of application problems. It is often difficult to compute union, intersection, and complements when it comes to a large number of members contained in the set, also it is difficult to check whether it is a subset or not. Here, we used the C-programming language to overcome the problems, and then it is found that more effective and realistic results have been obtained.

scholarly journals A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 142 ◽  
Author(s):  
Qianli Zhou ◽  
Hongming Mo ◽  
Yong Deng
Keyword(s):  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Distance Measure ◽  
Belief Function ◽  
Intuitionistic Fuzzy Sets ◽  
Divergence Measure ◽  
Pythagorean Fuzzy Sets ◽  
Practical Applications ◽  
Intuitionistic Fuzzy ◽  
Jensen Shannon Divergence

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.

scholarly journals The n-Pythagorean Fuzzy Sets

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1772
Author(s):  
Anna Bryniarska
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Quadratic Function ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Functions ◽  
Power Functions ◽  
Pythagorean Fuzzy Sets ◽  
Conceptual Apparatus ◽  
Intuitionistic Fuzzy ◽  
Classic Theory

The following paper presents deductive theories of n-Pythagorean fuzzy sets (n-PFS). N-PFS objects are a generalization of the intuitionistic fuzzy sets (IFSs) and the Yager Pythagorean fuzzy sets (PFSs). Until now, the values of membership and non-membership functions have been described on a one-to-one scale and a quadratic function scale. There is a symmetry between the values of this membership and non-membership functions. The scales of any power functions are used here in order to increase the scope of the decision-making problems. The theory of n-PFS introduces a conceptual apparatus analogous to the classic theory of Zadeh fuzzy sets, consistently striving to correctly define the n-PFS algebra.

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