A Hamacher Aggregation-Based Pythagorean Fuzzy Z-Number MCDM Framework for Sustainable Urban Green Space Planning
Evaluation of alternatives is a complex task in real-world decision-making, where ambiguity and uncertainty are inherent. To address these challenges, this study proposes an integrated Pythagorean Fuzzy Z-Number (PyFZN)-based framework for multi-attribute decision-making (MADM) in urban green space planning. PyFZNs extend intuitionistic fuzzy sets by incorporating both fuzzy membership information and reliability measures, enabling a more realistic representation of uncertainty and a more effective modeling of expert judgments. Hamacher norms with adjustable parameters are employed to improve the aggregation process, providing greater flexibility and consistency in information fusion. Based on these norms, a family of aggregation operators is developed to enhance decision-making performance under uncertain conditions. The proposed PyFZN-MADM framework is applied to evaluate urban green space alternatives using criteria such as population coverage, accessibility, environmental impact, cost, and social benefits. A metropolitan case study demonstrates the applicability of the proposed framework for ranking alternatives, optimizing resource allocation, and improving urban livability. The results indicate that the proposed approach is robust, sensitive, and reliable, outperforming existing methods in handling uncertainty and prioritizing alternatives. Comparative analysis further confirms its effectiveness in supporting informed, consistent, and reliable decision-making in complex urban planning environments.