An extended multi-criteria group decision-making method based on preference ranking under Z-number environments

Abstract

Compared with traditional fuzzy numbers, using Z-numbers to illustrate fuzzy events offers two key advantages. It makes fuzzy events more intuitive for decision-makers, and the second component of Z-numbers acts as a measure of the reliability of the first component. While significant progress has been made on Z-numbers, from the theoretical and practical perspectives, some gaps remain. For example, scholars have seldom focused on the likelihood of Z-numbers, most existing decision-making methods with Z-numbers rarely consider the consensus-reaching processes, and little has been reported on the superior ordering methods in the Z-number environment. To overcome these limitations, first, the likelihood of Z-numbers is defined in combination with the preference ranking organization method for enrichment evaluations (PROMETHEE) type V preference function. Second, the ordering rules for PROMETHEE are discussed. Then, a procedure of the feedback-adjustment method is introduced to help the consensus level of group-alternative ranking reach the threshold. On these bases, an extended PROMETHEE multi-criteria group decision-making method with Z-numbers is proposed. Finally, to verify the feasibility and effectiveness of the proposed method, we examined an intelligent medical-diagnostic-system selection problem and conducted a comparison analysis. We applied the Z-number PROMETHEE approach to a challenging case study requiring a dual-data-driven application. Furthermore, the study suggests future directions for improving the proposed framework in other related contexts.