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<p>The growing global wastewater crisis, driven by rapid urbanization, industrial expansion, and agricultural intensification, highlights the urgent need for efficient and sustainable treatment technologies. Selecting the most appropriate wastewater treatment solution is a complex, multidimensional decision-making problem characterized by uncertainty, interdependent criteria, and diverse expert judgments. To address these challenges, this study introduces a novel decision-making framework based on the spherical linear Diophantine fuzzy hypersoft set (SLDFHSS). This advanced fuzzy model integrates the structural properties of spherical linear Diophantine fuzzy sets (SLDFS) and fuzzy hypersoft sets (FHSS) to effectively represent and manage imprecise and uncertain information. Within this framework, two aggregation operators the spherical linear Diophantine fuzzy hypersoft weighted averaging (SLDFHSWA) and the spherical linear Diophantine fuzzy hypersoft weighted geometric (SLDFHSWG) operators are developed to combine evaluations from decision-makers with unequal weighting. A systematic multi-criteria decision-making (MCDM) algorithm is formulated to apply these operators for evaluating and ranking wastewater treatment alternatives. Comparative analysis demonstrates that the proposed framework outperforms existing methods in terms of accuracy, adaptability, and computational efficiency.</p>

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A Novel Decision-making Framework Based on Spherical Linear Diophantine Fuzzy Hypersoft Sets for Selecting Wastewater Treatment Technologies

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Pairote Yiarayong

摘要

The growing global wastewater crisis, driven by rapid urbanization, industrial expansion, and agricultural intensification, highlights the urgent need for efficient and sustainable treatment technologies. Selecting the most appropriate wastewater treatment solution is a complex, multidimensional decision-making problem characterized by uncertainty, interdependent criteria, and diverse expert judgments. To address these challenges, this study introduces a novel decision-making framework based on the spherical linear Diophantine fuzzy hypersoft set (SLDFHSS). This advanced fuzzy model integrates the structural properties of spherical linear Diophantine fuzzy sets (SLDFS) and fuzzy hypersoft sets (FHSS) to effectively represent and manage imprecise and uncertain information. Within this framework, two aggregation operators the spherical linear Diophantine fuzzy hypersoft weighted averaging (SLDFHSWA) and the spherical linear Diophantine fuzzy hypersoft weighted geometric (SLDFHSWG) operators are developed to combine evaluations from decision-makers with unequal weighting. A systematic multi-criteria decision-making (MCDM) algorithm is formulated to apply these operators for evaluating and ranking wastewater treatment alternatives. Comparative analysis demonstrates that the proposed framework outperforms existing methods in terms of accuracy, adaptability, and computational efficiency.