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<p>Sustainable water resource management has become a pressing challenge for Saudi Arabia due to rising demand, groundwater depletion, and environmental constraints. To evaluate and prioritize effective strategies under such complex conditions, this study develops an advanced multi-criteria decision-making (MCDM) framework. Interval-valued <i>q</i>-rung orthopair hesitant fuzzy (IV-qRHF) sets are adopted to capture uncertainty, hesitancy, and incomplete information in expert evaluations. A family of Hamacher-based operational laws tailored to the IV-qRHF environment is introduced. Building upon these laws, novel aggregation operators—namely the IV-qRHF Hamacher weighted averaging (IV-qRHFHWA) and IV-qRHF Hamacher weighted geometric (IV-qRHFHWG) operators—are proposed and their mathematical properties are examined. Several special cases of these operators are discussed to highlight their flexibility. In addition, an entropy measure is formulated and proven to satisfy the required axioms, serving as an objective tool for determining criteria weights when prior information is unavailable. By integrating the entropy measure with the proposed operators, a systematic MCDM framework is established. Its practicality is demonstrated via an applied analysis addressing long-term water sustainability challenges in Saudi Arabia. Sensitivity analysis confirms the stability of the model, while comparative experiments show its superiority over existing approaches, particularly in highly uncertain decision environments.</p>

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Entropy-Based Multi-attribute Decision Analysis with Hamacher Operators for Water Resource Management Challenges

  • 期刊论文

  • 发表日期：

    2026年7月21日

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  • Jawad Ali,
  • Ioan-Lucian Popa,
  • Ahmad N. Al-Kenani

摘要

Sustainable water resource management has become a pressing challenge for Saudi Arabia due to rising demand, groundwater depletion, and environmental constraints. To evaluate and prioritize effective strategies under such complex conditions, this study develops an advanced multi-criteria decision-making (MCDM) framework. Interval-valued q-rung orthopair hesitant fuzzy (IV-qRHF) sets are adopted to capture uncertainty, hesitancy, and incomplete information in expert evaluations. A family of Hamacher-based operational laws tailored to the IV-qRHF environment is introduced. Building upon these laws, novel aggregation operators—namely the IV-qRHF Hamacher weighted averaging (IV-qRHFHWA) and IV-qRHF Hamacher weighted geometric (IV-qRHFHWG) operators—are proposed and their mathematical properties are examined. Several special cases of these operators are discussed to highlight their flexibility. In addition, an entropy measure is formulated and proven to satisfy the required axioms, serving as an objective tool for determining criteria weights when prior information is unavailable. By integrating the entropy measure with the proposed operators, a systematic MCDM framework is established. Its practicality is demonstrated via an applied analysis addressing long-term water sustainability challenges in Saudi Arabia. Sensitivity analysis confirms the stability of the model, while comparative experiments show its superiority over existing approaches, particularly in highly uncertain decision environments.