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Weighted dual hesitant \(q\)-rung orthopair fuzzy sets and their application in multicriteria group decision making based on Hamacher operations

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Abstract

Dual hesitant q-rung orthopair fuzzy set has already been appeared as a useful tool to express fuzzy and ambiguous information more precisely than other variants of fuzzy sets. Usually, equal weights of the possible membership as well as non-membership values in a dual hesitant q-rung orthopair fuzzy set, are considered in modelling decision making problems, which is quite unreasonable. Because, in ascertaining possible membership or non-membership values for an alternative under some criteria, the frequency level of appearing those values frequently differs. Thus, employing same weights/ degrees of importance to each of the assigned membership and non-membership values would affect overall process of decision making. To overcome such situation, this paper introduces the notion of weighted dual hesitant q-rung orthopair fuzzy set which allows decision makers to assign different weights of possible arguments in details. Taking advantage of Hamacher t-norms and t-conorms as a generalization of algebraic and Einstein operations, some operational laws for weighted dual hesitant q-rung orthopair fuzzy sets are investigated in this paper. Further, based on those defined operational rules, a series of weighted aggregation operators are proposed to aggregate the weighted dual hesitant q-rung orthopair fuzzy information effectively. Next, applying the proposed operators, a methodology for solving real-life group decision making problems under weighted dual hesitant q-rung orthopair fuzzy context is developed. Lastly, the aptness of the introduced method is illustrated by solving few numerical examples.

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Authors and Affiliations

  1. Department of Mathematics, Heramba Chandra College, Kolkata, 700029, India

    Arun Sarkar

  2. Department of Mathematics, University of Kalyani, Kalyani, 741235, India

    Nayana Deb & Animesh Biswas

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  1. Arun Sarkar
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  2. Nayana Deb
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  3. Animesh Biswas
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Correspondence to Arun Sarkar.

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Sarkar, A., Deb, N. & Biswas, A. Weighted dual hesitant \(q\)-rung orthopair fuzzy sets and their application in multicriteria group decision making based on Hamacher operations. Comp. Appl. Math. 42, 40 (2023). https://doi.org/10.1007/s40314-022-02160-2

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