scholarly journals Effectiveness of Logarithmic Entropy Measures for Pythagorean Fuzzy Sets in diseases related to Post COVID Implications under TOPSIS Approach

2021 ◽  
Vol 9 (4) ◽  
pp. 178-183
Author(s):  
Yazar Adı Yazar Soyadı ◽  
Anjali Naithani
Keyword(s):  
Fuzzy Sets ◽  
Pythagorean Fuzzy Sets ◽  
Entropy Measures ◽  
Topsis Approach

scholarly journals Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision Making

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Miin-Shen Yang ◽  
Zahid Hussain
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Entropy ◽  
Entropy Measure ◽  
Pythagorean Fuzzy Sets ◽  
Entropy Measures ◽  
Criteria Weights ◽  
Ranking Of Alternatives ◽  
Probabilistic Type ◽  
Multicriterion Decision Making

The concept of Pythagorean fuzzy sets (PFSs) was initially developed by Yager in 2013, which provides a novel way to model uncertainty and vagueness with high precision and accuracy compared to intuitionistic fuzzy sets (IFSs). The concept was concretely designed to represent uncertainty and vagueness in mathematical way and to furnish a formalized tool for tackling imprecision to real problems. In the present paper, we have used both probabilistic and nonprobabilistic types to calculate fuzzy entropy of PFSs. Firstly, a probabilistic-type entropy measure for PFSs is proposed and then axiomatic definitions and properties are established. Secondly, we utilize a nonprobabilistic-type with distances to construct new entropy measures for PFSs. Then a min–max operation to calculate entropy measures for PFSs is suggested. Some examples are also used to demonstrate suitability and reliability of the proposed methods, especially for choosing the best one/ones in structured linguistic variables. Furthermore, a new method based on the chosen entropies is presented for Pythagorean fuzzy multicriterion decision making to compute criteria weights with ranking of alternatives. A comparison analysis with the most recent and relevant Pythagorean fuzzy entropy is conducted to reveal the advantages of our developed methods. Finally, this method is applied for ranking China-Pakistan Economic Corridor (CPEC) projects. These examples with applications demonstrate practical effectiveness of the proposed entropy measures.

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.

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 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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