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<p>In comparison with hesitant fuzzy sets and <i>q</i>-rung orthopair fuzzy sets, the dual hesitant <i>q</i>-rung orthopair fuzzy sets are more effective and flexible tool to deal with uncertainty and hesitation in decision-making problems. This article aims to propose a new variant of fuzzy set, viz., the dual hesitant <i>q</i>-rung orthopair trapezoidal fuzzy (DH<i>q</i>-ROTrF) set, and to develop a multicriteria group decision-making approach that employs DH<i>q</i>-ROTrF numbers (DH<i>q</i>-ROTrFNs) as evaluation values for capturing uncertainty and hesitation of expert judgments in a better way. The trapezoidal representation allows each evaluation to be expressed as a range rather than a single value, thereby improving the realism, flexibility, and robustness of uncertainty modelling compared to conventional dual hesitant <i>q</i>-rung orthopair fuzzy set. To begin with, this study proposes a set of fundamental operational laws for DH<i>q</i>-ROTrFNs based on Dombi <i>t</i>-norms and <i>t</i>-conorms. Using these operations, two novel aggregation operators, viz., the DH<i>q</i>-ROTrF Dombi weighted averaging operator and the DH<i>q</i>-ROTrF Dombi weighted geometric operator are introduced. The incorporation of Dombi operations enhances the flexibility and adaptability of the aggregation process in handling uncertainty and hesitation in group decision-making. In addition, various key aspects of the proposed operators are investigated. Furthermore, a new score function is formulated based on the concept of expected value to facilitate the ranking of alternatives. To demonstrate the application potentiality of the proposed method, a numerical example inspired by a real-life decision-making scenario for the recruitment of sales consultants is considered. The Criteria Importance Through Intercriteria Correlation (CRITIC) method is employed to determine the criteria weights, while the Weighted Aggregated Sum Product Assessment (WASPAS) method is used to rank the alternatives. Furthermore, the effects of the Dombi and rung parameters on the decision outcomes are thoroughly analysed to validate the robustness and practical usefulness of the developed approach. The findings confirm that the proposed framework can serve as an effective decision-support tool for complex group decision-making problems under uncertainty.</p>

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Development of dual hesitant q-rung orthopair trapezoidal fuzzy Dombi aggregation operators and their application in multi-criteria group decision making

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Apurba Mondal,
  • Souvik Gayen,
  • Animesh Biswas,
  • Arun Sarkar

摘要

In comparison with hesitant fuzzy sets and q-rung orthopair fuzzy sets, the dual hesitant q-rung orthopair fuzzy sets are more effective and flexible tool to deal with uncertainty and hesitation in decision-making problems. This article aims to propose a new variant of fuzzy set, viz., the dual hesitant q-rung orthopair trapezoidal fuzzy (DHq-ROTrF) set, and to develop a multicriteria group decision-making approach that employs DHq-ROTrF numbers (DHq-ROTrFNs) as evaluation values for capturing uncertainty and hesitation of expert judgments in a better way. The trapezoidal representation allows each evaluation to be expressed as a range rather than a single value, thereby improving the realism, flexibility, and robustness of uncertainty modelling compared to conventional dual hesitant q-rung orthopair fuzzy set. To begin with, this study proposes a set of fundamental operational laws for DHq-ROTrFNs based on Dombi t-norms and t-conorms. Using these operations, two novel aggregation operators, viz., the DHq-ROTrF Dombi weighted averaging operator and the DHq-ROTrF Dombi weighted geometric operator are introduced. The incorporation of Dombi operations enhances the flexibility and adaptability of the aggregation process in handling uncertainty and hesitation in group decision-making. In addition, various key aspects of the proposed operators are investigated. Furthermore, a new score function is formulated based on the concept of expected value to facilitate the ranking of alternatives. To demonstrate the application potentiality of the proposed method, a numerical example inspired by a real-life decision-making scenario for the recruitment of sales consultants is considered. The Criteria Importance Through Intercriteria Correlation (CRITIC) method is employed to determine the criteria weights, while the Weighted Aggregated Sum Product Assessment (WASPAS) method is used to rank the alternatives. Furthermore, the effects of the Dombi and rung parameters on the decision outcomes are thoroughly analysed to validate the robustness and practical usefulness of the developed approach. The findings confirm that the proposed framework can serve as an effective decision-support tool for complex group decision-making problems under uncertainty.