Uncertainty Measures Of Rules Based On Information Entropy And Variable Precision Rough Set

Rough set theory, firstly introduced by Zdzislaw Pawlak in 1982.is a new mathematical method to deal with vagueness, uncertainty knowledge and noise data. This approach has been used successfully in many fields, such as Machine Learning.Pattern Recognition. Knowledge Discovery, Expert Systems, Knowledge Acquisition, and Decision Support Systems.Rough set theory is based on indiscernibility relation imposed on the universe. This equivalence relation partitions all objects into a finite set of equivalence classes.Any subset of the universe can be approximately described by upper approximation and lower approximation which are sets of equivalence classes.The indiscernibility relation and boundary region (the difference from upper and lower approximation) generate the uncertainty when databases are dealt with by rough set algorithm.With the increase of this uncertainty, the number of deterministic rules will decrease, meanwhile, uncertainty of decision rules will increase.So it is significant to measure the uncertainty of rules.Duntsch.I gave three models for predicting the decision attribute.and defined different entropies-the measure of granular to describe uncertainty of decision rules.Xiang-Hui Chen proposed two entropies based on variable precision rough set theory. The two entropies make decision rules more robust.In this paper a new uncertainty measure of rules based on entropy and variable precision rough set is proposed to improve above-mentioned uncertainty measures, and applied to heuristic algorithms of attribute reduction.Comparing with one of Chen's entropies, the experiment results on CLEVE database show that the algorithm using the new uncertainty measure gets smaller attribute reduction and less decision rules with similar accuracy.