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

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. © 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.