New aggregation functions for spherical fuzzy sets and the spherical fuzzy distance within the MULTIMOORA method with applications

Abstract

This article develops a novel approach for multi-objective optimization on the basis of ratio analysis plus the full multiplicative form (MULTIMOORA) using spherical fuzzy sets (SFSs) to obtain proper evaluations. SFSs surpass Pythagorean and intuitionistic fuzzy sets in modeling human cognition since the degree of hesitation is expressed explicitly in a three-dimensional space. In the spherical fuzzy environment, the implementation of the MULTIMOORA encounters two major problems in the aggregation operators and the distance measures that might lead to erroneous results. The extant aggregation operators in some cases can result in a biased evaluation. Therefore, two aggregation functions for SFSs are proposed. These functions guarantee balanced evaluation and avoid false ranking. In the reference point technique, when comparing SFSs, being closer to the ideal solution does not necessarily imply an SFS with a better score. To make up for this drawback, two reference points are employed instead of one, and the distance is not expressed as a crisp value but as an SFS instead. To overcome the disadvantages of the dominance theory in large-scale applications, the results of the three techniques are aggregated to get the overall utility on which the ranking is based. The illustration and validation of the proposed spherical fuzzy MULTIMOORA are examined through two applications, personnel selection, and energy storage technologies selection. The results are compared with the results of other methods to explicate the adequacy of the proposed method and validate the results.