Uncertainty measures of rules based on entropy and variable precision rough set

The evaluation of the uncertainty of rough decision rules retrieved from a given data set needs proper uncertainty measures. Two new information entropy based uncertainty measures are presented based on variable precision rough set theory. They deal with the two aspects of uncertainty of rules coming from the granularity of the partition, namely inconsistency and randomness. Also they consider the influence of the noise in the data upon the consistency of the rules. As a result, they can propose some “nearly consistent rules”. A simple example is used to illustrate their fitness to evaluate rough decision rules retrieved from noisy data.