Abstract
The theory of three-way decision was originally introduced as three regions to explain rough sets. Nowadays we can apply this theory to many important fields by defining reasonable trisecting rules. In this paper, we reconsider the two-universe model of three-way decision proposed by Xu et al. and extend it to a more general level. Specifically, we introduce a pair of thresholds to the model and propose a generalized model of three-way decision with ranking and reference tuple. We prove that, although the pairs of thresholds are infinite, we only need to consider a finite number of pairs of thresholds and their corresponding trisections. Based on this theoretical foundation, we further define a unique measure to assess the trisections, compare trisections through this measure, and propose an algorithm to compute the optimal trisection in finite steps. By comparison with other models and an example of application, we demonstrate that the generalized model is more expressive and more practical than the previous one, and has some advantages over the compared models in accuracy of trisecting and validity of explaining.
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