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.

Introduction

Multiple Criteria Decision Making (MCDM) methodologies assist decision makers in choosing the best alternative while evaluating various competing and often conflicting criteria. Over the past many years, literature on MCDM has observed a steady growth [1] [2] while Analytical Hierarchical Process (AHP) proposed by Thomas L. Saaty [3] remains the most popular MCDM technique [4]. AHP seeks expert opinions in the form of pairwise comparisons and later derives ratio scales from comparison matrices which indicate the preferences of the decision maker among different alternatives in terms of the criteria as well as the preference i.e., weights of the criteria themselves. The normalized weighted sum over the criteria provides an overall score associated with each available alternative and thus help decision maker to choose the best decision. The vast literature on AHP is mainly divided based on two different scales that can be used to record pairwise comparisons namely, scale based on crisp numbers (scale of 1–۹) and scale based on fuzzy numbers. The original method as proposed by Saaty [3] uses the crisp scale of 1–۹ in which decision maker preferences assessed with natural language labels (e.g. weak, normal, strong etc.,) are represented by one crisp number in the given scale and recorded in comparison matrices. Whereas Fuzzy AHP (FAHP) algorithms use fuzzy numbers to represent the same preferences and they are recorded in corresponding fuzzy comparison matrices. Main motivation behind incorporating fuzzy set theory into original AHP is based on the argument that human judgments and preferences cannot be accurately represented by crisp numbers due to the inherent uncertainty in human perception. Disregarding this fuzziness of the human behavior in the decision making process may lead to wrong decisions [5]. Therefore, in order to address this issue of vagueness and uncertainty, and to accurately transform human judgments into ratio scales, fuzzy set theory introduced by Zadeh [6] has been extensively incorporated into the original AHP in which the weighing scale is composed of fuzzy numbers. In FAHP, weights are calculated from fuzzy