Confidence limits on rough set rules generated from a limited number of examples

The rough sets method is used for extracting both certain and possible rule s from data. This paper shows that, in reality, there are no certain rules. Probability theory is used to determine the best distribution to use when evaluating the strength of rules. A method of determining the confidence li mits for rules is presented, and this is used to determine what rule to fol low when conflicts occur. Finally, a way to apply these results to situatio ns where the cost of wrong decisions is different from the rewards for corr ect decisions is discussed.