Statistical evidence for rough set analysis

Rough set based rule induction methods have been applied to knowledge discovery in databases. The empirical results obtained show that they are very powerful and that some important knowledge has been extracted from datasets. However, quantitative evaluation of induced rules are based not on statistical evidence but on rather naive indices, such as conditional probabilities and functions of conditional probabilities. We introduce an approach to inducing rules for quantitative evaluation, which can be viewed as a statistical extension of rough set methods. For this extension, chi-square distribution and F-distribution play an important role in statistical evaluation