Global Supplier Selection with Spherical Fuzzy Analytic Hierarchy Process

Abstract

Spherical fuzzy sets (SFSs) have emerged lately as a new type of fuzzy sets in which the hesitancy degree is independent of the membership degree and the non-membership degree, thus providing a broader preference domain. This study extends the analytic hierarchy process (AHP) using (SFSs). In the proposed method, SFSs are used to construct the pairwise comparison matrices. Therefore, a spherical fuzzy preference scale is presented. Then, the consistency of the spherical fuzzy pairwise comparison matrices is checked to ensure obtaining a reasonable solution. To achieve this, the spherical fuzzy pairwise comparison matrices are converted to crisp matrices, and then Saaty’s eigenvalue method is applied to check the consistency. A prioritization function is proposed to determine the importance weights, hence construct the priority vector of the criteria and the priority vector of the alternatives for each criterion. Finally, the priorities of the alternatives obtained are combined in a weighted sum to form the global priority of each alternative. The alternative with the highest global priority is the best. The proposed method is used to solve an example in global supplier selection using SFSs and intuitionistic fuzzy sets (IFSs) to compare the results with the results of an intuitionistic fuzzy AHP.