Logical difference analysis based on variable precision lower approximation operator and graded upper approximation operator

This paper aims to construct and analyze an original logical difference based on the quantitative approximation operators. According to the variable precision lower approximation operator and graded upper approximation operator, we first put forward the specific logical difference; the new concept makes the specific logical combination on precision and grade, and has the practical multiple quantitative meaning. Then, both the fundamental structure and properties are investigated and obtained for the logical difference. Furthermore, two algorithms, the regular and structural algorithms, are proposed and analyzed, and the structural algorithm has more advantages. Finally, an example is provided. The proposed concept partially extends the graded and classical approximation operators; thus, some properties are achieved correspondingly for these previous approximation operators.