Mathematical Modeling of Wastewater Treatment Using Hybrid Neural Networks and Double Hierarchy Hesitant Fuzzy Archimedean–Dombi Operators

The selection of wastewater treatment (WWT) techniques requires a comprehensive evaluation of social, environmental, and economic factors. To enhance the robustness and interpretability of decision-making under uncertainty, this study introduces a novel framework based on the double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) for precise representation of experts’ hesitant and hierarchical linguistic judgments. To support this framework, we propose a double hierarchy hesitant fuzzy linguistic Archimedean–Dombi operator. In addition, we introduce the double hierarchy hesitant fuzzy linguistic Archimedean–Dombi average (DHHAA) operator, the double hierarchy hesitant fuzzy linguistic Archimedean–Dombi geometric (DHHGA) operator, and their weighted forms are formulated, with their key features. Furthermore, a hybrid fuzzy neural network-based multicriteria decision-making (MCDM) model that integrates these operators to effectively handle inconsistent or ambiguous information with learning-based adaptation. The proposed approach provides a powerful and intelligent decision-support mechanism for evaluating and selecting optimal WWT alternatives, thereby contributing to more adaptable and sustainable wastewater. Comparative and sensitivity analyses further validate the feasibility, robustness, and stability of the proposed method. The findings demonstrate the practical value of the approach, providing policymakers and environmental researchers with a systematic decision-support tool for implementing strategies on WWT.