Comparative Assessment of the Stability of AHP and FAHP Methods

Abstract

Mathematical models describing physical, technical, economic, and other processes can be used to analyze these processes and predict their results, providing that these models are stable and their results are stable relative to the model parameters used. Small changes in the values of the model parameters correspond to small changes in the results. Multicriteria decision-making models need to check the results’ stability against the models’ main components: the values of the criteria weights and the elements of the decision matrix. In this article, we study the stability of models associated with the calculation of criteria weights. For the analysis, the most commonly used models are taken—the Analytic Hierarchy Process (AHP) method and the fuzzy Analytic Hierarchy Process (FAHP) method, in which fuzzy numbers are used under conditions of data uncertainty. Both mathematically well-based methods verify the consistency of the expert evaluations. The method of statistical simulation (Monte Carlo) is the basis for studying the results’ stability. The study checks the experts’ provided evaluations’ consistency, calculates the criteria weights, and evaluates their relative errors after a slight change in the estimates of the pairwise comparisons of the criteria provided by the experts. The matrix of comparisons of the FAHP method is constructed based on the entire expert group’s assessments. It estimates the boundaries of variance in the fuzzy criteria weights. This paper estimates the stability of the criteria’ weights associated with the mathematical methods themselves and the experts’ estimates. The results are useful to study the stability of specific MCDM methods when ranking alternatives.

Decision support system for selecting tourist attractions using fuzzy analytic hierarchy process

“…FAHP method is a development of the AHP method. Crisp numbers of the AHP scale are considered less capable of handling uncertainty, so the original AHP scale must be approached by fuzzy logic [15], [16]. The development of FAHP was to overcome the uncertainty and subjectivity of input data more effectively than conventional MCDM techniques [17], [18].…”

A Product Shape Design and Evaluation Model Based on Morphology Preference and Macroscopic Shape Information

“…Mon et al [ 37 ] pointed out that the measurement of traditional AHP is too subjective, so an entropy weight-based FAHP was proposed. The implementation steps of FAHP are similar to conventional AHP, but FAHP needs to be defused and normalized [ 38 ]. In this article, the degree of consumer preference for shape is a fuzzy concept.…”

Application of Bayesian Approach to Reduce the Uncertainty in Expert Judgments by Using a Posteriori Mean Function

“…Considerable attention has been paid to verifying the stability of the methods themselves. Vinogradova has also researched the stability of decision-making methods, including Analytic Hierarchy Process (AHP), Fuzzy Analytic Hierarchy Process (FAHP) [3], Simple Additive Weighting (SAW), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Multi-objective Optimization (MOORA), and Preference ranking organization method for enrichment evaluation (PROMETHEE) [41,42], and the influence of data uncertainty on the final results. Ziemba uses stochastic analysis to study the uncertainty of the parameters of alternatives in the PROSA-C (PROMETHEE for Sustainability Assessment-Criteria) method [43].…”

“…In decision-making, particular attention is given to the uncertainty of the initial data. The uncertainty of the data can be estimated in different ways, depending on its source [3]. Methods have been developed for this purpose on the basis of specific mathematical theories such as fuzzy set theory and mathematical statistics [4].…”

“…Experts express their judgments in different ways. In particular, the information owned by the expert is extracted, and a probabilistic representation of this knowledge is constructed [15], using pairwise comparisons, linguistic variables, and fuzzy and natural numbers [3,9].…”