A study of cubical fuzzy possibility degree measure and its applications to multiple attribute decision-making problems

Abstract

In recent years, the extensions of fuzzy sets are much more familiar in almost all fields as they are reliable in defining the imprecise information of every decision-making situation. In this sequence of extensions, the cubical fuzzy sets are very efficient in dealing with imprecise information as it extends picture and spherical fuzzy sets. This article is interested in developing a new improved cubical fuzzy possibility degree measure. The desirable properties of the developed measure are also discussed. The advantage of the proposed measure is that it is capable of comparing the cubical fuzzy numbers in fuzzy nature itself and provides the degrees of preference relations between them. A comparison study is made with the existing ranking measures to exhibit the feasibility and validity of the proposed approach. Based on the improved measure, a method for ranking cubical fuzzy numbers is constructed. A solution approach to a cubical fuzzy multiple attribute decision-making problem is presented. To exhibit the potency and the practical applicability of the proposal, two real-life instances of selecting the best-cutting fluid for cutting gears have been illustrated. The results are compared with the literature.