Rough probability and rough expected value models

Rough set theory is a new and effective mathematical theory used for processing incomplete, uncertain and vague data. In this paper, new set-theoretic operators - rough operators are proposed based on Pawlak rough set. On the basis of rough operators, a self-duality measure -rough probability is presented. On the rough probability space, rough variable, rough distribution, and rough expected value are introduced, their some properties are given. Finally, rough expected value models are established, and the rough expected value model of the convexity theorem is proved.