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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 proved 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 a pair of necessity and possibility measures.
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 proven that for any belief structure and its inducing beliefs and plausibility measures there exists a random approximation space such that the associated lower and upper probabilities are 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 a pair of necessity and possibility measures.