In an uncertain context, extensions of the fuzzy set have a substantial impact in multiple criteria decision making (MCDM) situations. Cubical fuzzy set (CFS), is one such extension that is more advantageous for handling impreciseness in MCDM problems. The comparison of cubical fuzzy numbers (CFNs) is a signicant stage in the cubical fuzzy decision making process. In literature, it is found that the existing ranking functions fails to compare CFNs in certain situations. In order to address this issue, the current paper focuses on dening a new score function that compares CFNs in all circumstances. A comparison study is made with the literature to show the potency of the proposed score function. In multiple criteria problems, nding criteria weights plays a vital phase during the decision making process. Taking into account, this paper adopted the subjective method of pairwise comparison for determining the criteria objective weights. Further, a cubical fuzzy linear assignment method (CF-LAM) based on the proposed score function for solving a cubical fuzzy multiple criteria group decision making (CF-MCGDM) problem has been developed. The practical applicability and feasibility of the proposed score function using the developed LAM are illustrated by solving a real life MCGDM problem of nding the best location for the construction of a wind power farm under a CF environment.
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.
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