Determining Criteria Weights in MCDM Problems Using the Z-AHP Method

In this study, the Analytic Hierarchy Process (AHP) method used to determine the criteria weights in the integrated fuzzy multi-criteria decision-making (MCDM) approach developed by Erkayman et al. [1] for third-party logistics (3PL) provider selection has been re-examined using Z-numbers. The original model involves defining supplier selection criteria, determining their weights via fuzzy AHP, and ranking alternatives using the fuzzy TOPSIS method. A panel of experts, managers, and academics selected six key criteria—price, overall reputation, customer service, on-time delivery, information technologies, and flexibility—from an initial list of 30, and evaluated five alternatives out of 15 candidates. To capture the uncertainty in expert judgments, triangular fuzzy numbers were used in linguistic assessments. Z-numbers, proposed by Lotfi A. Zadeh [2], differ from classical fuzzy numbers by representing not only the uncertainty of a value but also the confidence level associated with that value. Mathematically, a Z-number is represented as Z=(A,B), where A is a fuzzy number reflecting the decision-maker's assessment, and B is another fuzzy number representing the degree of confidence in that assessment. Thus, Z-numbers more realistically capture the complexity of decision-makers' judgments. This study's primary contribution is the integration of the Z-number approach into the AHP step for calculating criteria weights. The relative importance levels of the six main criteria were represented as a pairwise comparison matrix whose elements are Z-numbers, derived by assigning hypothetical confidence levels to triangular fuzzy numbers. The resulting matrix was analyzed using an AHP method adapted for Z-numbers. This approach enables more precise and reliable determination of criteria weights, enhancing robustness in expert-based decisions.