Embedding Public Opinion in Sustainable Urban Infrastructure Planning: A Fuzzy–Grey Multi-Criteria Decision-Making Framework

Urban infrastructure planning is central to advancing sustainable cities, but project success increasingly depends on public acceptance as well as technical, economic, and environmental performance. This study develops a fuzzy–grey multi-criteria decision-making (MCDM) framework that embeds public opinion as a formal evaluation dimension. A novel POI, derived from online discourse data, integrates multi-dimensional emotions, polarization, and participation intensity to capture societal legitimacy. The framework employs entropy weighting and applies three established MCDM methods: TOPSIS, VIKOR, and EDAS, to evaluate project alternatives under uncertainty and incomplete information. An empirical case study in Nanjing demonstrates that incorporating Public Opinion Index (POI) significantly alters decision outcomes: the ecological park gained priority due to strong public support, while the wastewater treatment plant declined in ranking despite environmental benefits. These results underscore the decisive role of societal legitimacy in shaping sustainable infrastructure decisions. The framework contributes to sustainable urban planning by providing a replicable tool for balancing technical feasibility, environmental responsibility, and social acceptance in future infrastructure projects.