Three-way decisions based on multi-granulation support intuitionistic fuzzy probabilistic rough sets

Three-way decisions have become a representative of the models dealing with decision-making problems with uncertainty and fuzziness. However, most of the current models are single granular structures that cannot meet the needs of complex fuzzy environmental decision-making. Multi-granulation rough sets can better deal with fuzzy problems of multiple granularity structures. Therefore, three-way decisions will be a more reasonable decision-making model to address uncertain decision problems in the context of multiple granularity structures. In this paper, firstly we propose the four different conditional probabilities based on support intuitionistic fuzzy sets, which are referred to as support intuitionistic fuzzy probability. Then, a multi-granulation support intuitionistic fuzzy probabilistic approximation space is defined. Secondly, we calculate the thresholds a and beta by the Bayesian theory, and construct four different types of multi-granulation support intuitionistic fuzzy probabilistic rough sets models in multi-granulation support intuitionistic fuzzy probabilistic approximation space. Moreover, some properties of lower and upper approximation operators of these models are discussed. Thirdly, by combining these proposed models with three-way decision theory, the corresponding three-way decision models are constructed and three-way decision rules are derived. Finally, an example of person-job fit procedure is given to prove and compare the validity of these proposed models.