The Visual Analysis of Three-Way Decision Based on Decision-Theoretic Rough Set: A Perspective of Fusing Two-Way Decision Pair

Three-way decisions (3WDs) based on decision-theoretic rough set (DTRS), as a crucial theory in the field of granular computing, have received extensive attention. Meanwhile, visualization technologies have gained popularity, particularly for their intuitiveness and explainability. In order to understand the basic theory of 3WD more intuitively and enhance the interpretability analysis of threshold, this paper proposes the visual analysis of 3WD based on DTRS using the perspective of fusing two-way decision (2WD) pair. Firstly, the p-r space is defined via the geometric interpretations of the Bayesian decision procedure. Secondly, we propose a pair of 2WDs, i.e., the 2WD with acceptance and non-acceptance and the 2WD with rejection and non-rejection. And their geometrical interpretations are discussed in p-r space. Then, a fusing of the 2WD pair is proposed, and the geometric relations between its threshold and loss function are analyzed in p-r space. Finally, degeneration in the 2WD pair into the 3WD is obtained via the special loss function, which is employed to get the geometric interpretations for the threshold and loss function of single-evaluation-based 3WDs in p-r space. The method proposed in this paper uses the p-r space to obtain more intuitive explainability, which is more easily interpreted and reasoned of 3WD and has greater potential for generalization.