A Hamacher Aggregation-Based Pythagorean Fuzzy Z-Number MCDM Framework for Sustainable Urban Green Space Planning

Rani Sumaira Kanwal; Saqib Mazher Qurashi; Nasreen Kausar; Fatima Tul Zahra

doi:10.67334/cds31202637

Authors

Rani Sumaira Kanwal Department of Mathematics, Government College Women University, Faisalabad, Pakistan Author https://orcid.org/0009-0004-2424-4971
Saqib Mazher Qurashi Department of Mathematics, Government College University, Faisalabad, Pakistan Author https://orcid.org/0000-0002-4732-3320
Nasreen Kausar Department of Mathematics, Faculty of Arts and Science, Balikesir University, Türkiye Author https://orcid.org/0000-0002-8659-0747
Fatima Tul Zahra Department of Mathematics, Government College Women University, Faisalabad, Pakistan Author https://orcid.org/0009-0002-0760-3667

DOI:

https://doi.org/10.67334/cds31202637

Keywords:

Urban Green Space Planning, Pythagorean Fuzzy Z-Numbers, Criteria Decision-Making, Hamacher t-Norms, Multi-Criteria Decision-Making, Information Fusion, Uncertainty Modeling, Decision Support Systems, Urban Sustainability

Abstract

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.

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