Divergence measure of Pythagorean fuzzy sets and its application in medical diagnosis

A Pythagorean fuzzy set (PFS) is an extension of an intuitionistic FS that can be extended by relaxing the restriction on the grades of satisfaction and dissatisfaction. PFS is a powerful tool for dealing with uncertainty and vagueness. Correlation analysis of PFSs is a hot research topic in Pythagorean fuzzy (PF) theory and has practical applications in many areas, such as decision‐making, pattern recognition, medical diagnosis, engineering, and so forth. In this communication, we introduce some novel correlation coefficients in the PF‐environment satisfying the condition that the correlation coefficient of two PFSs is one if and only if the two sets are equal. We discuss the properties and applications of the proposed measures in pattern recognition, medical diagnosis, multicriteria decision‐making, and clustering analysis. Furthermore, the superiority of our proposed correlation coefficients over some existing ones is also established. We also extend the correlation coefficients to interval‐valued PFSs.

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“…Xiao and Ding

D_{1} true(P, Q true) = \frac{1}{2 n} \sum_{i = 1}^{n} false(false| {(α_{P} (u_{i}))}^{2} - {(α_{Q} (u_{i}))}^{2} false| + false| {(β_{P} (u_{i}))}^{2} - {(β_{Q} (u_{i}))}^{2} false| + false| {(γ_{P} (u_{i}))}^{2} - {(γ_{Q} (u_{i}))}^{2} false| false),

D_{2} true(P, Q true) = {\frac{1}{2 n} \sum_{i = 1}^{n} [{false({(α_{P} (u_{i}))}^{2} - {(α_{Q} (u_{i}))}^{2} false)}^{2} + {false({(β_{P} (u_{i}))}^{2} - {(β_{Q} (u_{i}))}^{2} false)}^{2} + false((γ_{P} (u_{i}

…”

Section: Applicationsunclassified

On some correlation coefficients in Pythagorean fuzzy environment with applications

Singh

Ganie

2020

Int J Intell Syst

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“…Later, a number of divergence measures between IFSs have been defined by various eminent researchers, 50,52,56–61 and the outcomes have been implemented in different application areas, including pattern recognition, decision‐making, medical diagnosis, image segmentation problems. In the Pythagorean fuzzy environment, Xiao and Ding 62 studied the Jensen‐Shannon divergence measure between PFSs and discussed its applications in medical diagnosis.…”

Section: Introductionmentioning

confidence: 99%

Multiple attribute group decision‐making based on order‐α divergence and entropy measures under q‐rung orthopair fuzzy environment

Verma

2020

Int J Intell Syst

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The q‐rung orthopair fuzzy set (qROPFS), proposed by Yager, is a more effective and proficient tool to represent uncertain or vague information in real‐life situations. Divergence and entropy are two important measures, which have been extensively studied in different information environments, including fuzzy, intuitionistic fuzzy, interval‐valued fuzzy, and Pythagorean fuzzy. In the present communication, we study the divergence and entropy measures under the q‐rung orthopair fuzzy environment. First, the work defines two new order‐α divergence measures for qROPFSs to quantify the information of discrimination between two qROPFSs. We also examine several mathematical properties associated with order‐α qROPF divergence measures in detail. Second, the paper introduces two new parametric entropy functions called “order‐α qROPF entropy measures” to measure the degree of fuzziness associated with a qROPFS. We show that the proposed order‐α divergence and entropy measures include several existing divergence and entropy measures as their particular cases. Further, the paper develops a new decision‐making approach to solve multiple attribute group decision‐making problems under the qROPF environment where the information about the attribute weights is completely unknown or partially known. Finally, an example of selecting the best enterprise resource planning system is provided to illustrate the decision‐making steps and effectiveness of the proposed approach.

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“…We can come to the conclusion that PFS can represent more uncertainty than IFS, consequently, PFS is more useful than IFS in MCDM issues. Furthermore, PFS has been extensively investigated from multiple perspectives, such as aggregation operators, decision methods and other applications …”

Section: Introductionmentioning

confidence: 99%

On Pythagorean fuzzy decision making using soft likelihood functions

2019

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Multicriteria decision making (MCDM) is to select the optimal candidate which has the best quality from a finite set of alternatives with multiple criteria. One important component of MCDM is to express the evaluation information, and the other one is to aggregate the evaluation results associated with different criteria. For the former, Pythagorean fuzzy set (PFS) is employed to represent uncertain information in this paper, and for the latter, the soft likelihood function developed by Yager is used. To address MCDM issues from a new perspective, the likelihood function of PFS is first proposed in this study and, to improve some of its limitations, the ordered weighted averaging (OWA)‐based soft likelihood function is defined, which introduces the attitudinal characteristic to identify decision makers' subjective preferences. In addition, the defined soft likelihood function of PFS is extended by weighted OWA operator considering the importance weight of the argument. Several illustrative cases are provided based on the presented (weighted) OWA‐based soft likelihood functions in Pythagorean fuzzy environment for MCDM problem.

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Divergence measure of Pythagorean fuzzy sets and its application in medical diagnosis

Cited by 245 publications

References 66 publications

On some correlation coefficients in Pythagorean fuzzy environment with applications

On some correlation coefficients in Pythagorean fuzzy environment with applications

Multiple attribute group decision‐making based on order‐α divergence and entropy measures under q‐rung orthopair fuzzy environment

On Pythagorean fuzzy decision making using soft likelihood functions

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