Three-way decision on information tables

The model of three-way decision on two universes generalizes various two-universe models of rough sets, and it is in fact defined on 0-1 tables, i.e. binary information tables. This paper generalizes the model of three-way decision from 0-1 tables to general information tables. The framework of three-way decision on general information tables is presented and the connection of existing related models is investigated. In our models, every element in the set of objects is assigned to a value and we can construct a tri-partition of the object set according to a pair of thresholds. We present a fundamental result of the models, which induces two concepts: the fundamental sequence and pair. On the one hand, the fundamental result shows that there exist finitely many pairs of thresholds. That is, we need only to consider the case of finitely many tri-partitions. On the other hand, it describes how the positive region varies based on thresholds and induces a concept of positive region tower. Finally, we evaluate these finite tri-partitions by the weighted entropy, which is a new measure defined as a variant of information entropy. An optimal tri-partition can be obtained according to weighted entropies of the finite tri-partitions. (C) 2020 Published by Elsevier Inc.