Entropy based uncertainty measures for classification rules with inconsistency tolerance

As an uncertainty data analysis method, rough set theory can be used to retrieve classification rules from the given data by partitioning the data according to the indiscernibility relations. The evaluation of uncertainty of rough classification rules needs some proper uncertainty measures. The uncertainty coming from the granularity of the partition includes inconsistency and randomness. Unlike the approximation quality of rough sets, the information entropy based uncertainty measures can deal with the two aspects of uncertainty. On the other hand, the noise in the given data can make the inconsistency overestimated. As a result, some originally consistent rules may become inconsistent and be rejected improperly. Inspired by variable precision rough set model, we construct two new uncertainty measures, which have some tolerance for the inconsistency of the data. Experimental results illustrate the fitness of them to evaluate the classification rules retrieved from the noisy data