Two novel three-way decision models based on fuzzy -covering rough sets and prospect theory under q-rung orthopair fuzzy environments

Three-way decision (TWD) and prospect theory (PT) are efficacious theories for investigating uncertain problems. TWD can mitigate the risks associated with rapid decision-making in traditional decision-making. PT can describe the psychological behavior of decision-makers. Furthermore, q-rung orthopair fuzzy sets (q-ROFSs) exhibit wider-ranging applications since they generalize intuitive fuzzy sets and Pythagorean fuzzy sets and unify them under one framework. However, the acquisition of q-ROFSs is an important issue in practical problems. In light of these considerations, this paper develops two TWD models under q-rung orthopair fuzzy environments, employing the principles of PT. To begin, we introduce two novel fuzzy beta-covering rough sets that meet the inclusion property. Subsequently, utilizing the proposed fuzzy rough set, we provide an objective methodology to acquire q-ROFSs. Following this, the relative utility function is given through a combination of the value function and EDAS method. Additionally, the weighting function is constructed using two distinct approaches: one that continues to incorporate the ideas of EDAS method, and the other that utilizes the probabilistic dominance beta-neighborhood classes to calculate conditional probabilities. After that, classification rules and sorting rules are derived. Ultimately, we substantiate the validity and excellence of the proposed TWD models through comparative and experimental analysis.