Accuracy and coverage in rough set rule induction

Rough set based rule induction methods have been applied to knowledge discovery in databases, whose empirical results obtained show that they are very powerful and that some important knowledge has been extracted from datasets. For rule induction, lower/upper approximations and reducts play important roles and the approximations can be extended to variable precision model, using accuracy and coverage. However, the formal characteristics of accuracy and coverage for rule induction have never been discussed. In this paper, several following characteristics of accuracy and coverage are discussed: (1) accuracy and coverage measure the degree of sufficiency an necessity, respectively. Also, they measure that of lower approximation and upper approximation. (2) Coverage can be viewed as likelihood. (3) These two measures are related with statistical independence. (4) These two indices have trade-off relations. (5) When we focus on the conjunction of attribute-value pairs, coverage decreases more than accuracy.