Decision framework with integrated methods for group decision-making under probabilistic hesitant fuzzy context and unknown weights

A hesitant fuzzy set is a flexible generalization of a fuzzy set that permits agents to furnish multiple views and the occurrence probability of each element is either the same or unknown. However, in our day-to-day problems, such an assumption is always narrow. The researchers state a concept of probabilistic hesitant fuzzy set (PHFS) to handle this. Based on the previous studies on PHFS, specific gaps can be identified, such as (i) agents' weights are not methodically determined, (ii) approaches for criteria weights do not consider criteria interrelationship and the importance of agents, (iii) preferences are aggregated without considering the agents' discrimination factors, risk appetite, and interdependencies, (iv) Broad/moderate rank values with reduced rank reversal phenomenon during prioritization is not taken. To overcome these drawbacks, in this article, we presented a new decision- making approach in which an attitude-based Shannon entropy and regret/rejoice approach is utilized to calculate the criteria and agents' weights, respectively. Further, a variance-based Muirhead mean operator is proposed by considering the interdependencies and variations to aggregate the different preferences represented in PHFS. Finally, an approach based on the WASPAS ("Weighted Arithmetic Sum Product Assessment") method is presented to rank the different objects. The proposed framework is demonstrated with a numerical example and compares their results with the several existing studies' results to reveal the framework's superiority.