A regret-theory-based three-way decision method with a priori probability tolerance dominance relation in fuzzy incomplete information systems

In real world, decision-makers’ regret psychology often affects decision outcomes due to uncertain risks. Moreover, decision information may be missing in the process of data acquisitions or data storages. Three-way decision has been widely explored in the risky decision-making area by providing effective strategies to divide objects into three mutually disjoint regions. Existing three-way decision methods in fuzzy incomplete information systems rarely consider the influence of decision-makers’ psychological states on decision outcomes. In the current paper, we primarily study a new decision-making method that combines regret theory with three-way decision in fuzzy incomplete information systems. First, a prior probability tolerance dominance relation in a fuzzy incomplete information system is defined to handle a binary relation among evaluation values, and a method to calculate objective weights is designed as well. When an incomplete information system does not contain a fuzzy decision attribute value, we put forward a new method to calculate the decision attribute value of each object in the incomplete information system. Then, integrated utility perception values are obtained by combining with regret theory. Further, a regret theory-based three-way decision method with a priori probability tolerance dominance relation is proposed for fuzzy incomplete information systems. At last, the stability and validity of the presented method are verified via corresponding experimental and comparative analysis of realistic cases.