Valued outranking relation-based heterogeneous multi-decision multigranulation probabilistic rough set and its use in medical decision-making

Regarding to group decision-making, decision makers may express different decision preferences for the same target. Since existing decision-making methods only consider a single decision preference at most, it is difficult to integrate the multi-decision preferences of multiple decision makers effectively. In this paper, we explore a class of heterogeneous multi-attribute group decision-making (MAGDM) problems with multiple decisions. Over the framework of granular computing, we present a new MAGDM method with the aid of the valued outranking relations in the ELECTRE III method. Considering the non-compensability among attributes, we first define a special valued outranking relation on a heterogeneous attribute multi-decision information system, and then present the notion of valued outranking classes. Subsequently, given the fact that the fault tolerance of probability approximations can reduce the vulnerability of decision-making methods, we construct multi -decision multigranulation probabilistic rough sets (MD-MGPRSs) form different perspectives, which extend existing rough set models to a more general situation. After that, we establish a novel MAGDM method, and apply the method to a real medical case to illustrate its applicability. Lastly, the experimental results on seven datasets demonstrate the effectiveness, robustness, and superiority of the method. Our study not only enriches the theoretical research of rough sets, but also extends the application scope of decision-making theory.