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

Nayana Deb, Arun Sarkar and Animesh Biswas ()
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Nayana Deb: University of Kalyani, Department of Mathematics
Arun Sarkar: Heramba Chandra College, Department of Mathematics
Animesh Biswas: University of Kalyani, Department of Mathematics

Chapter Chapter 19 in q-Rung Orthopair Fuzzy Sets, 2022, pp 505-555 from Springer

Abstract: Abstract 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.

Keywords: Dual hesitant $$q$$ q -rung orthopair fuzzy sets; Interval-valued dual hesitant $$q$$ q -rung orthopair fuzzy sets; Heronian mean; Geometric Heronian mean; Aggregation operator; Multicriteria decision-making (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-19-1449-2_19

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DOI: 10.1007/978-981-19-1449-2_19

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