Abstract: Based on logical AND requirement of precision and grade, a logical AND operation model of variable precision lower approximation operator and grade upper approximation operator was proposed. In the new model, precise description and basic properties were obtained. Macroscopic algorithm and microscopic algorithm were proposed and analyzed, and a conclusion was made that microscopic algorithm had advantages in space complexity. Finally the new model and the algorithms were illustrated by a medical example. The new model has extended variable precision rough set model, graded rough set model and classical rough set model partially, and corresponding properties of approximation operators are obtained in these models.

Key words: rough set model, variable precision rough set, graded rough set, approximation operator, logical operation

摘要： 基于精度与程度的逻辑与需求，提出了变精度下近似算子与程度上近似算子的逻辑与运算模型。在该模型中，得到了变精度下近似算子与程度上近似算子的逻辑与运算的精确描述与基本性质，提出了宏观算法与微观算法，进行了算法分析与比较，得到了微观算法更具空间优势的结论。最后用医疗实例对模型与算法进行了说明。变精度下近似算子与程度上近似算子的逻辑与运算模型，部分拓展了变精度粗糙集模型、程度粗糙集模型和经典粗糙集模型，并在这些模型中得到了近似算子的相应性质。

关键词: 粗糙集模型, 变精度粗糙集, 程度粗糙集, 近似算子, 逻辑运算