Further Discussions on Rough Probability and Rough Random Variables

Rough set is a new mathematical tool to handle problems of imprecision, uncertainty, and vagueness. The phenomena of roughness and randomness appear at the same time in our real world, but the rough set can not deal with the case, so it is essential to establish a rough probability theory to handle these phenomena. The rough probability theory is further discussed in this paper. Firstly, rough probability on rough probability space is further discussed. Secondly, the concepts of distribution function, expected value and variance of the rough random variables on the rough probability space are given, and some properties are discussed. This paper makes rough probability theory perfect further on the rough probability spaces.