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Real-life decision making based on a new correlation coefficient in Pythagorean fuzzy environment

P. A. Ejegwa|J. A. Awolola
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2021.02|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제21권 제1호|pp. 51-67|DOI 10.30948/afmi.2021.21.1.51

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키워드

Intuitionistic fuzzy setDecision-makingPattern recognitionPythagorean fuzzy setCorrelation coefficient measureMedical diagnosis

초록

Pythagorean fuzzy set (PFS) is a generalized version of intuitionistic fuzzy set (IFS) with the capacity to manage the situation that cannot be captured by IFS. PFS is characterized by three grades namely; membership grade, non-membership grade and hesitancy grade with the property that the square of sum of the grades is equal to one. The idea of correlation coefficients for measuring the interrelationship between PFSs have been proposed in literature. Nonetheless, these sort of correlation coefficients for PFSs lack precision. Due to this weakness, a new correlation coefficient for PFSs is introduced in this paper. In this study, the Garg's correlation coefficient for PFSs is generalized and modified for better accuracy. Some interesting properties of the proposed correlation coefficient for PFSs are characterized with some results. A set of numerical examples are given to demonstrate the efficiency of the introduced correlation coefficient for PFSs with regard to the existing ones. It appears that the proposed correlation coefficient for PFSs outperforms the ones hitherto studied in literature. Subsequently, some real-life decision-making (RLDM) problems such as pattern recognition problem (e.g., classification of mineral fields) and diagnostic medicine in the framework of Pythagorean fuzzy pairs are discoursed with the aid of the new correlation coefficient. This proposed measuring tool could be exploited in multi-criteria decision-making problems via object oriented approach.

Abstract

Pythagorean fuzzy set (PFS) is a generalized version of intuitionistic fuzzy set (IFS) with the capacity to manage the situation that cannot be captured by IFS. PFS is characterized by three grades namely; membership grade, non-membership grade and hesitancy grade with the property that the square of sum of the grades is equal to one. The idea of correlation coefficients for measuring the interrelationship between PFSs have been proposed in literature. Nonetheless, these sort of correlation coefficients for PFSs lack precision. Due to this weakness, a new correlation coefficient for PFSs is introduced in this paper. In this study, the Garg's correlation coefficient for PFSs is generalized and modified for better accuracy. Some interesting properties of the proposed correlation coefficient for PFSs are characterized with some results. A set of numerical examples are given to demonstrate the efficiency of the introduced correlation coefficient for PFSs with regard to the existing ones. It appears that the proposed correlation coefficient for PFSs outperforms the ones hitherto studied in literature. Subsequently, some real-life decision-making (RLDM) problems such as pattern recognition problem (e.g., classification of mineral fields) and diagnostic medicine in the framework of Pythagorean fuzzy pairs are discoursed with the aid of the new correlation coefficient. This proposed measuring tool could be exploited in multi-criteria decision-making problems via object oriented approach.

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