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<p>In multi-criteria decision making (MCDM), abundant fuzzy and uncertain information poses significant challenges. Although the Fermatean fuzzy set offers a useful framework for representing such uncertainty, its ability to quantify information remains limited. To address this gap, this study proposes an enhanced Fermatean fuzzy set integrated with the Dempster–Shafer theory (DST) for more effective uncertainty quantification. Furthermore, two novel aggregation operators are introduced: the Fermatean fuzzy power partitioned Hamy mean operator under DST (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({FFPP}_{t}H{M}_{DST}^{q}\)</EquationSource> </InlineEquation>) and its weighted counterpart (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({FFWPP}_{t}H{M}_{DST}^{q}\)</EquationSource> </InlineEquation>). These operators not only incorporate the power average (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(PA\)</EquationSource> </InlineEquation>) and partitioned mean (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({P}_{t}M\)</EquationSource> </InlineEquation>) mechanisms to mitigate bias from subjective evaluative judgments, but also utilize the Hamy mean (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(HM\)</EquationSource> </InlineEquation>) to capture interrelationships among multiple criteria. A new MCDM approach is developed based on the proposed framework and validated through a real-world case study on hotel selection. Comparative analyses confirm that the method achieves notable improvements in both flexibility and interpretability over existing techniques, demonstrating its practical applicability and broader relevance to complex decision-making scenarios.</p>

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Multi-criteria decision making in the improved fermatean fuzzy set based on DST and its application

  • 期刊论文

  • 发表日期：

    2026年2月21日

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  • Jialong He,
  • Tianshuo Yu,
  • Yan Liu,
  • Zhenbiao Ma

摘要

In multi-criteria decision making (MCDM), abundant fuzzy and uncertain information poses significant challenges. Although the Fermatean fuzzy set offers a useful framework for representing such uncertainty, its ability to quantify information remains limited. To address this gap, this study proposes an enhanced Fermatean fuzzy set integrated with the Dempster–Shafer theory (DST) for more effective uncertainty quantification. Furthermore, two novel aggregation operators are introduced: the Fermatean fuzzy power partitioned Hamy mean operator under DST ( \({FFPP}_{t}H{M}_{DST}^{q}\) ) and its weighted counterpart ( \({FFWPP}_{t}H{M}_{DST}^{q}\) ). These operators not only incorporate the power average ( \(PA\) ) and partitioned mean ( \({P}_{t}M\) ) mechanisms to mitigate bias from subjective evaluative judgments, but also utilize the Hamy mean ( \(HM\) ) to capture interrelationships among multiple criteria. A new MCDM approach is developed based on the proposed framework and validated through a real-world case study on hotel selection. Comparative analyses confirm that the method achieves notable improvements in both flexibility and interpretability over existing techniques, demonstrating its practical applicability and broader relevance to complex decision-making scenarios.