Two Rough Set Operators Based on the Neighborhood Systems and its Applications

In present paper, we give two rough set new operators based on the neighborhood system, under this two operators, the two important inequalities in rough set theory is modified to become equalities. The usefulness information will not be lost. In the other hand, it is also decreased the mistake information. Meanwhile, we also discuss the roughness and precision of a fuzzy set in the generalized approximation space based on the two rough set operators. In the same time, some usefulness properties are discussed and the conclusion which in present paper given are improved and extended the conclusion in the current literatures.