A Weighted Uncertainty Measure of Rough Sets Based on General Binary Relation

Uncertainty measure is one of the important aspects of rough set theory.A new kind of weighted uncertainty measure calledα-entropy is presented under general binary relation by considering the sample data with different importance,and some existing uncertainty measures are a special case ofα-entropy by adjusting the variable parameterα.Thus it unites the corresponding uncertainty measures of complete and incomplete information systems.In addition,a well-justified uncertainty measures,α-roughness(α-accuracy)is proposed based onα-entropy.It is proved thatα-roughness(α-accuracy)decreases(increases)monotonously as the information granularities become smaller.The numerical example proves that theα-accuracy andα-roughness are more reasonable and accurate than the existing methods.Finally,under general binary relation,a new heuristic weighted attribute reduction algorithm is proposed based onα-accuracy. The experiments demonstrate that the weighted measures in this paper provide a method for combining the subjective preferences and prior knowledge in uncertainty measures,and the combination classifier based on the variable parameterαcan improve the accuracy of classification.These investigations developed the uncertainty theory and provide theory basis for knowledge acquisition in information systems based on general binary relation.