Modified Expressions to Evaluate the Correlation Coefficient Between Two Dual Hesitant Fuzzy Soft Sets and Their Application in Decision-Making

Abstract

This paper is the study of the existing correlation coefficients (CCoefs) to evaluate the meaningful relation/dependency between two variables of the extended fuzzy sets for solving decision-making (DeM) problems. To understand the weighted CCoefs between two variables the considered domain is the dual hesitant fuzzy soft set (DHFSS) which is an extension of a fuzzy set incorporating properties of both the dual hesitant fuzzy set (DHFS) (which considers the hesitancy degree of both the membership and non-membership elements of a set) and soft set (SS) (which gives the importance to each parameter in an alternative). This strive suggests improved weighted CCoefs for solving DHFSS problems from the existing weighted CCoefs for solving DHFSS multi-criteria decision-making (MCDM) problems (DeM problems in which the rating value of each alternative over each criterion is depicted by a DHFSS) in a real-world. Also, mathematical verification is presented which clearly states the validation of the proposed expressions of weighted CCoefs for solving DHFSS MCDM problems. To show the practical application of the proposed weighted CCoefs for solving DHFSS MCDM problems, solutions to some real-world problems like- recruitment, medical diagnosis, and pattern recognition are determined, and a methodical comparison of the results are shown between the considered real-life MCDM problems by the existing approach and by the proposed approach interpretation.