Three-way decisions in ordered decision system

As a natural extension of three-way decisions, this paper presents a novel three-way decision model with order information. First, we do some comparative analysis between ordered three-way decisions and decision-theoretic rough sets, and then present some important properties of the proposed model. Second, a hybrid decision table consisted both of the “order information” and “loss function”, is utilized to solve the ordered three-way decisions with two classification problem. Two order sets (dominating set and dominated set generated by order relation) and three risk strategies (optimistic strategy, equable strategy, pessimistic strategy) are induced to construct the model and design the algorithm of ordered three-way decisions. At last, an illustrative example of salary administration validates the reasonability and effectiveness of our approach.