A three-way decision model in incomplete ordered information systems with fuzzy pre-decision

The three-way decision model has been extended by many researchers in recent years to allow its application to a wide range of datasets. The three-way decision model in incomplete ordered information systems is the focus of this paper. First, we estimate the missing values in an incomplete ordered information system to obtain a complete ordered information system with confidence. Second, according to the ideas of TOPSIS method and regret theory, the dominance relations based on PIS and NIS respectively are defined. Then, according to the idea of TOPSIS method, the fuzzy pre-decision and relative loss function matrix are defined. The fuzzy pre- decision and dominance relations are utilized to calculate the degree of objects belonging to PIS class and NIS class. Finally, the expected loss of executing different decisions is calculated and three-way decision rules are induced by Bayesian minimum risk decision theory. The associated properties of the rules are discussed and the rationality of the model is explained. In the experimental section of the paper, we design two sets of experiments aimed at categorizing and ordering the objects according to the proposed algorithm, thus providing a deeper insight into the feasibility and superiority of the three-way decision model.