Incremental fuzzy probabilistic rough sets over two universes

The fuzzy Information System over Two Universes (ISTU) formalizing a data table corresponding to two universes as well as their relations is common in real-world applications, e.g., recommender system and clinical diagnosis system. The fuzzy probabilistic rough sets over two universes (FPRSMTU) can deal with a fuzzy relation and allow a tolerance inaccuracy in the construction of rough approximations in a fuzzy ISTU, which is a generalization of classic rough sets with fuzzy and probabilistic theories. As a necessary step for knowledge discovery based on rough sets, the fuzzy rough approximations of fuzzy ISTU need to be updated efficiently under dynamic data environment. Incremental technique is an efficient approach for dynamic information processing by making full use of previously obtained knowledge. In this paper, incremental approaches for updating approximations of fuzzy ISTU are proposed while some objects adding into or deleting from the two universes, and the corresponding incremental algorithms are designed. Experimental evaluations on real datasets as well as artificial datasets show the effectiveness of the proposed incremental updating method compared with the non-incremental method.