Advancing group decision-making in sustainable water resource management: a Z-number enhanced framework for wastewater reuse

In the face of global water scarcity, sustainable water resource management, such as treated wastewater reuse, is crucial. However, identifying optimal reuse alternatives presents significant challenges, primarily due to the complexities of decision-making under uncertainty, conflicting criteria, and varying expert judgments. This paper introduces a Group Multi-Attribute Decision-Making (GMADM) method enhanced with Z-numbers, a new generation of fuzzy logic that effectively manages uncertainties by incorporating data constraints and expert judgment reliability. A key contribution of this study is the development of a method to convert linguistic variables and pairwise comparisons into a Z-number-driven Decision Matrix (ZDM), improving the decision-making process in complex group scenarios. To address computational challenges, a simplified approach to calculating Z-numbers is proposed, which reduces computational costs.

The method is applied to a case study on Tabriz, Iran, a city facing significant water scarcity. Five wastewater reuse alternatives are evaluated based on nine sub-criteria spanning economic, technical, environmental, and social factors. The Z-number-driven GMADM method ranks alternatives using fuzzy Hausdorff distance (FHD) and relative closeness (RC) to ideal solutions. A comparison with traditional methods, such as the fuzzy analytic hierarchy process (FAHP), shows that industrial usage is ranked as the top alternative for wastewater reuse. The sensitivity analysis confirms that variations in expert opinion reliability significantly impact the rankings of alternatives, further validating the proposed method’s applicability in real-world decision-making scenarios, particularly in sustainable water resource management.