Abstract: We studied a power inclusion degree on fuzzy sets and established the fuzzy rough set model based on it with the foundation of weak fuzzy partition. Some important properties of this model were approached and the method to compute the roughness correspondingly was illustrated. Furthermore, two roughness measures of fuzzy rough set in this model were defined according to the Hamming-distance and Euclid-distance. The fuzzy rough set model we proposed can carry the computing on fuzzy rough set by fuzzy sets operating properties. And this model can lay the theoretical founlotion for research and applications of variable precision fuzzy rough set,

Key words: Inclusion degree, Fuzzy set, Rough set, Variable precision fuzzy rough set, Roughness measure