Novel Generalized Distance Measure of Pythagorean Fuzzy Sets and a Compromise Approach for Multiple Criteria Decision Analysis under Uncertainty

Abstract

This paper aims at developing a novel generalized distance measure of Pythagorean fuzzy (PF) sets and constructing a distance-based compromise approach for multiple criteria decision analysis (MCDA) within PF environments. The theory of Pythagorean fuzziness provides a representative model of nonstandard fuzzy sets; it is valuable for representing complex vague or imprecise information in many practical applications. The distance measure for Pythagorean membership grades is important because it can effectively quantify the separation between PF information. Based on the essential characteristics of PF sets (membership, non-membership, strength, and direction), this paper proposes several distance measures, namely, new Hamming and Euclidean distances and a generalized distance measure that is based on them for Pythagorean membership grades and for PF sets. Moreover, the useful and desirable properties of the proposed PF distance measures are investigated to evaluate their advantages and form a solid theoretical basis. In addition, to evaluate the performance of the proposed distance measures in practice, this paper establishes a PF-distance-based compromise approach for addressing MCDA problems that involve PF information. The effectiveness and practicability of the developed approach are further evaluated through a case study on bridge-superstructure construction methods. According to the application results and comparative analysis, the proposed PF distance measures are accurate and outperform other methods in handling the inherent uncertainties of evaluation information. Furthermore, the PF-distance-based compromise approach can accommodate the much higher degrees of uncertainty in real-life decision scenarios and effectively determine the priority ranking among candidate alternatives for managing complicated MCDA problems.