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<p>This study introduces a novel method for evaluating fractional double hierarchy linguistic term sets (FDHLTs) in three-way decision-making (TWD) contexts. The suggested methodology combines the first and second levels of linguistic term sets (LTSs) to mitigate uncertainty and ambiguity frequently present in intricate decision-making situations. A thorough collection of aggregation operators and operational principles designed for FDHLTs, encompassing Hamacher-type operators, a distance metric, and a scoring system, is presented to enhance the framework. A decision-theoretic rough set (DTRS) model is developed, utilizing grey relational analysis (GRA) within the FDHLTS framework to calculate conditional probabilities (CPs) for improved decision accuracy. To quantitatively assess the efficacy and resilience of the suggested method, sensitivity analysis was performed by varying criterion weights, demonstrating superior stability in ranks relative to traditional techniques such as TOPSIS, WASPAS, and COCOSO. Statistical metrics, such as mean absolute deviation (MAD) of CPs and Spearman’s rank correlation coefficients, further validate that the FDHLTS-TWD framework ensures consistent and dependable decision results while offering enhanced interpretability. The methodology establishes optimal selections by employing the minimum-loss principle in conjunction with a loss function. A case study assessing a transportation program and logistics service provider illustrates the practical applicability, stability, and effectiveness of the proposed framework in mitigating uncertainty and facilitating informed decision-making.</p>

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A novel three-way decision-making framework based on fractional double hierarchy linguistic term sets

  • 期刊论文

  • 发表日期：

    2026年3月7日

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  • Muhammad Awais,
  • Muhammad Sajjad,
  • Faisal Mehmood,
  • Muhammad Mukhtar Qureshi

摘要

This study introduces a novel method for evaluating fractional double hierarchy linguistic term sets (FDHLTs) in three-way decision-making (TWD) contexts. The suggested methodology combines the first and second levels of linguistic term sets (LTSs) to mitigate uncertainty and ambiguity frequently present in intricate decision-making situations. A thorough collection of aggregation operators and operational principles designed for FDHLTs, encompassing Hamacher-type operators, a distance metric, and a scoring system, is presented to enhance the framework. A decision-theoretic rough set (DTRS) model is developed, utilizing grey relational analysis (GRA) within the FDHLTS framework to calculate conditional probabilities (CPs) for improved decision accuracy. To quantitatively assess the efficacy and resilience of the suggested method, sensitivity analysis was performed by varying criterion weights, demonstrating superior stability in ranks relative to traditional techniques such as TOPSIS, WASPAS, and COCOSO. Statistical metrics, such as mean absolute deviation (MAD) of CPs and Spearman’s rank correlation coefficients, further validate that the FDHLTS-TWD framework ensures consistent and dependable decision results while offering enhanced interpretability. The methodology establishes optimal selections by employing the minimum-loss principle in conjunction with a loss function. A case study assessing a transportation program and logistics service provider illustrates the practical applicability, stability, and effectiveness of the proposed framework in mitigating uncertainty and facilitating informed decision-making.