Rule extraction is a main goal for rough set theory. This paper mainly constructs a new algorithm (LBRM Algorithm) for rule extraction based on rough membership. The confidence principle is established based on rough membership. Thus, LBRM Algorithm is proposed by utilizing discretization and clearness strategies under the fuzzy environment, and is applied to both interval rules and general rules in fuzzy classification. LBRM Algorithm effectiveness is illustrated by a medical example. In particular, LBRM Algorithm integrates the confidence on both previous LBR Algorithm and fundamental rough membership, and has some improvements on rule confidence.

This paper aims to construct new operation of approximation operators, and explore its calculation. First it proposes logical difference operation of variable precision lower approximation operator and grade upper approximation operator. Then regular algorithm and structural algorithm are proposed and analyzed, and furthermore, a conclusion is drawn that structural algorithm has advantages in time complexity and space complexity. Finally a practical example is given to illustrate the new operation and its algorithms.

Grade is an important index for quantitative research, and graded rough set model is an important extended rough set model. This paper aims to study logical AND operation of grade approximation operators and its algorithms in graded rough set model. Based on logical AND requirement of grade index, logical AND operation of grade approximation operators is proposed and analyzed, and its essence and basic structure are obtained. Both conventional algorithm and microscopic algorithm are proposed and analyzed, and a conclusion is drawn that microscopic algorithm has more advantages in contrast to conventional algorithm. Finally, logical AND operation of grade approximation operators and its algorithms are illustrated by an example.