Abstract: The basic idea of the three-way decisions (3WD) is ‘thinking in threes.’ The TAO (trisecting-acting-outcome) model of 3WD includes three components, trisect a whole into three reasonable regions, devise a corresponding strategy on the trisection, and measure the effectiveness of the outcome. By reviewing existing studies, we found that only a few papers touch upon the third component, i.e., measure the effect. This paper’s principal aim is to present an effectiveness measure framework consisting of three parts: a specific TAO model - Change-based TAO model, interval sets, and utility functions with unique characteristics. Specifically, the change-based TAO model provides a method to measure effectiveness based on the difference before and after applying a strategy or an action. First, we use interval sets to represent these changes when a strategy or an action is applied. These changes correspond to three different intervals. Second, we use the utility measurement method to figure out three change intervals. Namely, different utility measures correspond to the different intervals, concave utility metric, direct utility metric, and convex utility metric, respectively. Third, it aggregates the toll utility through the joint of the three utilities mentioned above. The weights among these three are adjusted by a dual expected utility function that conveys the decision-makers’ preferences. We give an example and experiment highlighting the validity and practicability of the utility measure method in the change-based TAO model of three-way decisions.
