Rough Set Approximations Based on Random Sets

In this paper, the concept of a random rough set which includes the mechanisms of numeric and non-numeric aspects of uncertain knowledge is introduced. It is shown that for any belief structure and its inducing belief and plausibility measures there exists a random approximation space such that the associated lower and upper probabilities are respectively the given belief and plausibility measures, and vice versa. And for a random approximation space generated from a totally random set, its inducing lower and upper probabilities are respectively necessity and possibility measures.