General three-way decision models on incomplete information tables

In this paper, we propose general three-way decision models on incomplete information tables. First, for an incomplete information table, we give an axiomatic definition of similarity degree functions on a single attribute. By use of extended aggregation functions, similarity degree functions on an attribute set are also proposed. Then we define a new kind of similarity class of objects and study its properties . On the basis of this similarity class, general three-way decision models based on two evaluation functions and one evaluation function on incomplete information tables are established, respectively. In addition, we study the properties of these general three-way decision models. Finally, we compare the general model based on one evaluation function and a pair of thresholds with four existing models. The results show that the four existing models can be regarded as special cases of this general model, which illustrates the rationality of the new proposed models.