Measure Effectiveness of Change-based Three-way Decision Using Utility Theory

The trisecting-acting-outcome (TAO) model of three-way decision plays a crucial role in solving complex problems. It comprises three components: trisecting, acting, and outcome. Trisecting means dividing an entire set into three relatively small parts based on an evaluation function, and acting means designing the corresponding action to apply to these three parts. The outcome denotes evaluation effectiveness based on the first two steps. Several previous investigations have measured effects from a coarse-grained perspective. Still, they have not considered the impact of fine-grained changes in objects and have not devised the method of selecting a strategy-constructed tripartition for a given expected outcome. The present study aimed to explore the outcome measure from the view of fine-grained changes in objects named change-based three-way decision. It also provides a novel approach to quantifying outcomes using utility theory. Specifically, we conducted the study using two perspectives: top-down and bottom-up, depending on the decision demands. The object is first divided into three regions based on changes corresponding to different utilities from the top-down view. Then, the overall utility is aggregated based on the particular utility metrics representing different satisfaction levels in the three regions. From the bottom-up perspective, we derive a pair of thresholds based on the desired utility of the decision-maker and thus obtain three parts whose changes can make by some action to achieve these effects. The principal conclusions of this exploration are that outcomes can be better ranked using objects' changes using utility theory and that strategies can be better acting to achieve corresponding variations based on the expected utility of the decision-maker. We describe the specific steps and procedures of the proposed method through several examples. The findings presented in this paper add to our understanding of the outcome measure for the three-way decision.