Statistical tests for multiplicative consistency of fuzzy preference relations: A Monte Carlo simulation

Fuzzy preference relation (FPR) models the preference information provided by decision-makers using pairwise comparison of alternatives. The extant consistency test of FPRs, as a premise of expert opinions aggregation, suffers from the rule unfairness problem in different cases. Specifically, it is too loose in the lower-order cases and too strict in the higher-order cases. To address this issue, two statistical tests for the multiplicative consistency of FPRs are proposed. Based on multiplicative transitivity, an indirect average-based consistency index is proposed to allow for perturbed weights without an arbitrary choice of the weight derivation approach. This improves the robustness of the analysis of the consistency of the FPRs as results for a particular FPR no longer depend on the choice of the weight derivation approach. Moreover, the Monte Carlo simulation is applied to derive the sampling distribution of the indirect average-based consistency index. Two multiplicative consistency tests for the FPRs are proposed. In this context, the probabilities of Type I and Type II errors are governed by significance levels. Finally, the numerical examples and comparative analysis illustrate the effectiveness of the proposed consistency tests.