Interval‐Valued Probabilistic Dual Hesitant Fuzzy Muirhead Mean Aggregation Operators and Their Applications in Regenerative Energy Source Selection

As an effective addition to the hesitant fuzzy set (HFS), a probabilistic dual hesitant fuzzy set (PDHFS) has been designed in this paper. PDHFS would be an improved version of the dual hesitant fuzzy set (DHFS) where both membership and nonmembership hesitant quality is considered for all its probability of existence. Additional information on the degree of acceptance or rejection contains such allocated probabilities. More conveniently, we create a comprehensive type of PDHFS called interval‐valued PDHFS (IVPDHFS) to interpret the probability data that exist in the hesitancy. This study describes several basic operating laws by stressing the advantages and enriching the utility of IVPDHFS in MAGDM. To aggregate IVPDHF information in MAGDM problems and extend its applications, we present the Muirhead mean (MM) operator of IVPDHFSs and study some attractive properties of the suggested operator. Besides that, in order to compute attribute weights, a new organizational framework is designed by using partial knowledge of the decision makers (DMs). Subsequently, a standardized technique with the suggested operator for MAGDM is introduced, and the realistic usage of the operator is illustrated by the use of a problem of regenerative energy source selection. We discuss the influence of the parameter vector on the ranking results. Finally, to address the benefits and limitations of the recommended MAGDM approach, the findings of the proposal are contrasted with other approaches.