Interval-Valued Spherical Fuzzy Z-AHP Method Based on Reliability of Judgments: Green Supplier Selection

Fuzzy sets have been widely used for many multi-criteria decision-making problems including vague and imprecise information of decision makers. In order to provide a broader definition of uncertainty, fuzzy sets have been expanded to various versions in recent years. Z-fuzzy numbers are capable of reflecting the reliability information through restriction and reliability functions. In addition to reliability factor, there is a need for a decision-making methodology that can take into account the hesitancy of experts. Spherical fuzzy sets (SFSs) which let experts assign membership degrees from a larger domain give this methodology a more flexible structure. In this paper, SFSs are used to develop a new fuzzy Z-AHP method. We propose a novel Interval-valued Spherical Fuzzy Z-Analytic Hierarchy Process (IVSF Z-AHP) by integrating the IVSF sets and Z-fuzzy numbers. We also propose a new IVSF Z linguistic scale and a new defuzzification formula which provide an objective and consistent scoring for decision makers’ pairwise comparison matrices. Finally, an application is performed for green supplier selection problem to illustrate the application of the proposed methodology. Comparative analysis and sensitivity analysis are also given to explicitly show the necessity of reliability information in decision making. The results show that the proposed method is very effective in determining the best alternative with reliability and hesitancy information.