Properties of Approximation operators of logical AND operation of precision and grade

Precision and grade are two important indexes for quantitative research. This paper is to research relationship and combination between precision and grade, and explore new extended rough set model. First it obtains relationship and transformation formulas between variable precision approximations and grade approximations. Then based on logical AND operation of precision and grade, rough set model of logical AND operation of precision and grade is proposed. In the new model, approximation operators of logical AND operation of precision and grade are studied, and their propertion are obtained, such as the power action. The new rough set model has extended variable precision rough set model, graded rough set model and classical rough set model, graded rough set models have classical rough set model, and so these rough set models have obtained the corresponding power action of approximation operators.