Triangular Z-Numbers Using Centroid Method: A Case Study of Flood Mitigation Measures

Abstract

Z-numbers offer a robust framework for modeling human reasoning under uncertainty by integrating both a constraint and a reliability component. Despite their theoretical strengths, the practical application in Fuzzy Multi-Criteria Decision Making (FMCDM) has been limited due to the complexity of Z-numbers arithmetic and the lack of an effective defuzzification method that can preserve information during conversion to crisp values. To address these challenges, this study proposes a novel FMCDM methodology that employs triangular Z-numbers, a simplified representation to improve computational efficiency. The centroid method is adopted for defuzzification, selected for its ability to preserve the information during defuzzification process. This proposed methodology enhances both the computational feasibility and practical usability of Z-numbers, allowing decision-makers to express their judgments and confidence levels without relying on complex mathematical formulations. The effectiveness of the proposed methodology is demonstrated through a case study on flood mitigation measures, showing its ability to produce reliable and consistent rankings of alternatives. Comparative analysis with existing methods further validates the robustness and applicability of the proposed methodology, making it a viable tool for complex decision-making processes.