Logical or model of variable precision upper approximation operator and grade lower approximation operator

Precision and grade are two important quantitative indexes. This paper is to combine precision and grade, and explore new extended rough set model. Based on logical OR requirement of precision and grade, this paper proposes logical OR model of variable precision upper approximation operator and grade lower approximation operator. In the new model, basic structure and properties are obtained by transformation formulas between variable precision approximations and grade approximations, furthermore regular algorithm and structural algorithm are proposed and analyzed. Finally a practical example is given to illustrate the model and the algorithms. The new model has extended variable precision rough set model, graded rough set model and classical rough set model, and so these models have obtained corresponding properties of approximation operators.