Model of logical or operation of variable precision lower approximation operator and grade upper approximation operator

Precision and grade are two important quantitative indexes. The purpose of this paper is to combine precision and grade, and explore new extended rough set model. Based on logical OR operation of precision and grade, this paper proposes model of logical OR operation of variable precision lower approximation operator and grade upper approximation operator. In the new model, fundamental structure and properties are obtained by transformation formulas between variable precision approximations and graded 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 similar properties of approximation operators.