Fuzzy Analytic Hierarchy Process: A Performance Analysis of Various Algorithms

Abstract

Abstract Analytical Hierarchical Process (AHP) along with fuzzy set theory has been used extensively in the Multi-Criteria Decision Making (MCDM) process in which fuzzy numbers are utilized to represent human judgments more realistically. Over the past couple of decades, numerous articles have been published proposing algorithms through which priority vector (or weight vector) can be calculated from fuzzy comparison matrices. The aim of this study is to conduct a comprehensive performance analysis of the most popular algorithms proposed in this domain in terms of accuracy of weights calculated from fuzzy comparison matrices. Such an analysis is much needed by the researchers and practitioners. However none is available. An experimental analysis is conducted and the performance of various algorithms are evaluated with varying three parameters i.e., the size of the comparison matrix, the level of fuzziness and the level of inconsistency. We found that modified Logarithmic Least Squares Method and Fuzzy Inverse of Column Sum Method (FICSM) generally outperformed other algorithms, while Fuzzy Extent Analysis (FEA) which is the most frequently used algorithm in the literature provides the least accurate results. Furthermore, it was observed that a modified version of FEA method significantly improved its performance.