Evaluation of Advanced Drinking Water Treatment Technologies using Pythagorean Fuzzy Hypersoft Set-Based Multi-Criteria
Abstract
Securing safe and reliable drinking water increasingly requires the adoption of advanced treatment technologies whose performance depends on heterogeneous technical, economic, environmental, and regulatory factors. This work proposes a novel multi-criteria decision-making (MCDM) framework based on Pythagorean fuzzy hypersoft sets (PFHSS) for ranking drinking water treatment technologies under complex, uncertain judgments of experts. Ten technologies— microfiltration, ultrafiltration, nanofiltration, reverse osmosis, forward osmosis, ion exchange, electrodialysis, electrodialysis reversal, electrode ionization, and desalination—are evaluated with respect to 10 criteria: technology requirement, health impact, economy, environmental impact, quantity requirement, legal aspects, ease of operation and maintenance, energy requirements, treatment versatility, and efficiency. Unlike classical AHP-TOPSIS combinations, the proposed PFHSS model allows experts to express degrees of membership, non-membership, and hesitation at the sub-attribute level for each criterion while preserving the soft decomposition of parameter sets into mutually disjoint sub-parameters. Aggregation operators and a PFHSSbased score function are developed to obtain a global ranking of technologies. Mathematical proofs establish the validity of the operators and scoring mechanisms. A numerical illustration using the qualitative pattern of previously published data shows that electrodialysis reversal and electrodialysis remain among the top-ranked options, while the PFHSS framework yields more nuanced insight into uncertainty and hesitancy in expert judgments.