Evaluation functions and decision conditions of three-way decisions with game-theoretic rough sets

Three-way decisions have been used over the years in many application areas. The rough sets and its extensions provide useful approaches for three-way decisions. Typically, these approaches employ a single evaluation function or criterion to induce three-way decisions. When extending the rough set based three-way decisions to multiple criteria decision making (MCDM), two issues are encountered. The first issue is related to the construction and definition of aggregation mechanisms for dealing with differences in results of evaluation functions. The second issue is related to the setting of choice structure for selecting the three types of decision choices. In this article, we consider the role and use of game-theoretic rough set (GTRS) model to resolve and address these two issues. The issue related to differences in evaluation functions is addressed with GTRS by implementing a game that considers multiple evaluation functions as game players. The game-theoretic analysis in the GTRS is employed to resolve the differences by determining a tradeoff between evaluation functions. The issue related to choice structure is addressed by considering the conditions under which different game outcomes could constitute a game solution. In particular, the equilibrium analysis within games is used to construct the rules for three-way decisions. A demonstrative example is used to explain the use of the proposed approach. The relationship between the proposed approach and the probabilistic rough sets is also discussed.