Information Measures for Continuous Function-Valued q-Rung Orthopair Fuzzy Sets and an Extended TOPSIS

Abstract

The concept of continuous function-valued [Formula: see text]-rung orthopair fuzzy set (CFV[Formula: see text]ROFS) represents an innovative framework within fuzzy set theory, where the assessment of an element’s membership and nonmembership degrees is accomplished through continuous functions. This paper introduces a novel entropy measure for CFV[Formula: see text]ROFS, employing the Riemann integral. Furthermore, it outlines a theoretical framework for constructing a similarity measure based on entropy and presents a distance measure. The newly introduced entropy measure is used for weighting criteria and measuring the distance of the alternatives in decision-making processes. To illustrate the practical utility of these concepts, an extended Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is proposed and is employed to tackle a real-world problem previously addressed in the literature. The outcomes of this extended TOPSIS are compared with those given in existing studies, and a sensitivity analysis is performed concerning the variable [Formula: see text].