A novel complex (p,q,r)- spherical fuzzy TOPSIS framework for sustainable urban development assessment

Abstract

Sustainable urban development (SUD) projects aim to enhance infrastructure, services, and facilities in cities to improve residents’ quality of life, promote economic growth, and ensure long-term sustainability. As urbanization accelerates globally, decision-makers face significant challenges in selecting projects that balance environmental, economic, social, and technological factors while aligning with strategic urban planning goals. The complexity of these decisions is further heightened by uncertainties in stakeholder opinions, evolving policy frameworks, and real-world constraints. To address these challenges, this study introduces a multi-criteria group decision-making (MCGDM) framework designed specifically for evaluating SUD projects. The proposed methodology leverages complex $(p,q,r)-$ spherical fuzzy sets (${\mathrm{Com}}_{(p,q,r)}$ SFSs) to provide a more flexible and adaptive decision-making structure. These fuzzy sets allow decision-makers to model varying degrees of membership with greater adaptability, ensuring a more precise and comprehensive evaluation of alternatives. The primary contribution of this study lies in its parametric approach, which enhances the dynamism and adaptability of decision-making in complex urban development scenarios. To achieve this, the study is structured into three phases. First, we introduce the fundamental notations and operational laws of ${\mathrm{Com}}_{(p,q,r)}$ SFSs, followed by the development of aggregation operators to handle uncertainty in expert evaluations. In the second phase, we construct a TOPSIS-based approach utilizing these aggregation operators, enabling systematic ranking of SUD project alternatives. The effectiveness of the proposed approach is demonstrated through a numerical example evaluating five alternatives across seven criteria, capturing key factors influencing sustainable urban planning. Finally, the results are compared with existing decision-making methodologies to validate the robustness, effectiveness, and applicability of the proposed framework. By providing a structured, data-driven, and adaptable approach, this study aims to assist urban planners and policymakers in making more informed, balanced, and sustainable decisions for future urban development.