Development of Heronian Mean-Based Aggregation Operators Under Interval-Valued Dual Hesitant q-Rung Orthopair Fuzzy Environments for Multicriteria Decision-Making

Interval-valued dual hesitant $$q$$ q -rung orthopair fuzzy (IVDH $$q$$ q -ROF) set (IVDH $$q$$ q -ROFS) is a new variant of fuzzy set that can depict uncertain and imprecise situations more adequately than other existing fuzzy variants. In solving complicated multicriteria decision-making (MCDM) problems, decision-makers (DMs) sometimes confront interdependent aggregated arguments. Heronian mean (HM) can successfully capture the interrelationships between input arguments. The aim of this chapter is to define a new MCDM method under IVDH $$q$$ q -ROF environment based on HM operator. The proposed method is not only capable of dealing with DMs’ hesitancy in a wide range but also can handle complicated decision-making situations by capturing interrelations among the aggregated arguments. In model formulation, at first, some HM-based IVDH $$q$$ q -ROF aggregation operators, viz., IVDH $$q$$ q -ROF HM, IVDH $$q$$ q -ROF weighted HM, IVDH $$q$$ q -ROF geometric HM, and IVDH $$q$$ q -ROF weighted geometric HM operators are proposed. Additionally, justifications of those operators to act as aggregation operators are validated by proving some of their desirable properties. Subsequently, a methodology for solving MCDM problems having interrelated input information is developed using the proposed operators. Further, a numerical example is solved to verify the application validity of the proposed approach. Finally, a comparative study with the existing approaches is performed to show the effectiveness of the developed method.