A novel surface fuzzy analytic hierarchy process

Abstract

For almost fifty years, the concept of fuzzy analytic hierarchy process based on triangular fuzzy numbers, supplied with various types of membership functions has experienced a wide variety of Intuitionistic fuzzy numbers, z-Numbers, and Spherical fuzzy numbers. This paper aims to upgrade the concept of Spherical Fuzzy Sets considering the hesitancy, its third coordinate, as a function instead of constant. This broads the decision-makers "spectrum" allowing them to describe the fuzzy part of data more comprehensively. As a path distance between two fuzzy sets, we used geodesic lines in place of great circles, connecting Fuzzy logic with Differential geometry. Also, we proved some algebraic properties concerning associativity and neutral elements for operations ⊕ and ⊗, for the defined Surface Fuzzy Sets. Additionally, the application of Surface Fuzzy Sets to within AHP is used for ranking Security, Privacy, and Authority sub-criteria affecting B2C e-commerce websites.