Intuitionistic Fuzzy Analytic Network Process

Abstract

Since the analytic network process (ANP) is much more flexible than the analytic hierarchy process in handling the multiple criteria decision making (MCDM) problems in which the criteria or subcriteria are interdependent, it has attracted many scholars’ attention and has been applied into many different areas. Given the powerfulness of intuitionistic fuzzy set in representing positive, negative, and indeterminate information, this paper investigates the ANP framework for the MCDM problems in which all the pairwise comparison judgment information over the objects are represented by intuitionistic fuzzy numbers. We first justify the way to decompose the MCDM problem into a holarchy and network structure, based on which, the intuitionistic fuzzy preference relations (IFPRs) can be constructed through pairwise comparisons over the goals, criteria, clusters as well as the elements. Considering that not all the IFPRs are consistent, we then propose a new method to derive the priorities from the IFPRs no matter the IFPRs are consistent or not. After that, we address the way to construct the supermatrix for those interdependent elements. The complete algorithm of intuitionistic fuzzy ANP (IFANP) is given and illustrated by a flow chart. To show the applicability and efficiency of the IFANP, we implement the method to a case study concerning the brand management of the six golden flowers of Sichuan liquor. Some comparative analyses are given to clarify the advantages and invalidation of the IFANP.