Decision framework study demonstrates consistent ranking outcomes in arid smart water management, highlighting robust multi-attribute decision-making under complex uncertainty.
Multi-attribute decision-making (MADM) problems often involve uncertain, bipolar, and complex-valued information that cannot be adequately represented by conventional fuzzy models. Although bipolar complex Pythagorean fuzzy sets (BCPFSs) provide a powerful framework for handling such information, they lack mathematically consistent formulations and effective aggregation mechanisms. To address these limitations, this paper presents a revised bipolar complex Pythagorean fuzzy framework and develops novel Dombi operational laws based on t-norm and t-conorm concepts. Using these operations, two aggregation operators, namely the bipolar complex Pythagorean fuzzy Dombi weighted average (BCPFDWA) and bipolar complex Pythagorean fuzzy Dombi weighted geometric (BCPFDWG) operators, are proposed for aggregating bipolar complex Pythagorean fuzzy information. A corresponding MADM approach is then established and applied to a smart water resource management problem in arid regions. The results demonstrate that the proposed operators produce consistent and reliable ranking outcomes under different parameter settings. Comparative and sensitivity analyses further confirm the flexibility, robustness, and effectiveness of the proposed framework, highlighting its suitability for complex decision-making problems involving bipolar and complex-valued uncertainty.
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Ibrahim et al. (2026) studied this question.
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