Statistical test for rough set approximation based on Fisher's exact test

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. However, quantitative evaluation of lower and upper approximation are based not on statistical evidence but on rather naive indices, such as conditional probabilities and functions of conditional probabilities. In this paper, we introduce a new approach to induced lower and upper approximation of original and variable precision rough set model for quantitative evaluation, which can be viewed as a statistical test for rough set methods, For this extension, chi-square distribution, F-test and likelihood ratio test play an important role in statistical evaluation. Chi-square test statistic measures statistical information about an information table and F-test statistic and likelihood ratio statistic are used to measure the difference between two tables.