Projection based regret theory on three-way decision model in probabilistic interval-valued q-rung orthopair hesitant fuzzy set and its application to medicine company

Three-way decision (3WD) can be used to handle complexity and uncertainty in decision-making problems, and is compatible with human cognitive systems. For insufficient existing experiences, decision-makers (DMs) can select interval fuzzy information, as the information about medicine company is more hesitation, imprecision, and ambiguity. In the determination process, DMs may not take suitable decisions by choosing membership and non-membership degree of imprecise information. To improve fault-tolerance and validate the plausibility of DMs’ evaluation, the probabilistic interval-valued q-rung orthopair hesitant fuzzy set (PIVq-ROHFS) is introduced. Additionally, distinct psychological behaviours of DMs have an impact on the outcomes of decision-making. For this situation, we first develop a regret theory based 3WD model in PIVq-ROHFS to evaluate the utility value of the objects. The core focus of regret theory is to develop a new regret-rejoice function based on projection theory. Another core focus of this inquisition is to propose a novel multi-criteria decision making (MCDM) method for evaluating conditional probability in 3WD model. The criteria’s weight in MCDM method is evaluated by a newly proposed multi-objective optimization (MOO) problem. To solve the MOO problem, we utilize a hybrid technique by combining particle swarm optimization and multi-choice goal programming with utility function.