Three-way decisions with fuzzy probabilistic covering-based rough sets and their applications in credit evaluation

Abstract

As a generalization of equivalent class, fuzzy covering makes descriptions of the objective world more realistic, practical and accurate in some cases. In this paper, we establish four kinds of fuzzy probabilistic covering-based rough set, which combine the fuzzy covering-based neighborhood operator and the fuzzy probabilistic rough set, and then obtain the result of their three-way decision. The differences among the above models lie in the selection of thresholds, which further leads to different classification results. In addition, in order to interpret the thresholds rationally under different models, Bayesian decision procedure is adopted to construct the fuzzy probabilistic covering-based upper and lower approximation operators. Finally, a numerical example of the credit evaluation is applied to illustrate the validity of the proposed model.