Regret-based three-way decisions with set pair analysis in incomplete information systems

Abstract

Set pair analysis is a valuable tool for managing uncertain systems and can effectively handle missing information in the decision-making process. In addition, regret theory can objectively describe the impact of decision-maker psychology on decision-making. However, traditional decision-making methods rarely combine set pair analysis and regret theory to discuss decision problems. Thus, this article aims to integrate regret theory into the three-way decision theory based on set pair analysis, presenting a novel approach to address multi-attribute decision-making problems in real life. Specifically, we first propose a data-driven approach based on set pair analysis to determine attribute weights. Then, a similarity relationship is established based on the weighted distance to calculate conditional probability. Meanwhile, the average value of regret and joy under each attribute is selected as a reference point to determine the relative utility function using regret theory. Subsequently, we develop a new three-way decision method in incomplete information systems and apply it to solve practical problems. Finally, the effectiveness and superiority of our method are demonstrated by case analysis and comparison. We also conduct sensitivity analysis to examine the stability of the new method.