Fractional orthopair fuzzy decision framework for sustainable water resource management in urban areas

Sustainable urban water management is increasingly challenged by uncertainty, imprecision, and hesitancy in evaluating alternative water sources. This study proposes a novel multi-criteria decision-making (MCDM) framework based on fractional orthopair fuzzy (FOF) sets, designed to model partial hesitancy and fractional expert judgments more effectively than traditional fuzzy methods. Integrating an entropy-based weighting scheme and the technique for order preference by similarity to ideal solution (TOPSIS), the framework is applied to assess water resource alternatives in Lahore, Pakistan a city facing rapid groundwater depletion, urban expansion, and declining surface water quality. The evaluation considers three key criteria: water quality, availability, and affordability across the alternatives of surface water, groundwater, and rainwater. Results show that rainwater harvesting is the most sustainable option, with a closeness coefficient of [Formula: see text], outperforming alternatives in terms of both cost-effectiveness and safety. Sensitivity analysis on parameters ([Formula: see text], [Formula: see text]) confirms the model's robustness. The findings offer actionable guidance for water authorities, emphasizing the importance of rainwater harvesting and reduced reliance on depleting groundwater. The proposed model is adaptable to other urban regions, provided expert input and contextual data are available.