Weighted Reduction for Decision Tables

Abstract

As a classical problem of Rough Sets, the reduct problem still attracts research interests recently. Many existing works on the reduct problem are devoted into finding optimal reducts where the optimal metrics is the number of attributes. In reality, however, this optimal metrics is not fair since some attributes may have much larger domains than others, and they tend to have better discernibility thus more likely to be included in optimal reducts. To cope with this fairness problem, in this paper we propose the concept of average discernibility which takes into consideration the cardinality of the attribute domain. Attribute reduction based on average discernibility can be implemented through assigning each attribute an appropriate weight in the reduction process to adjust attribute significance. We point out further that some human experts knowledge can also be expressed by the weight vector formed by weights of all attributes. Then we propose a weighted reduction algorithm based on discernibility, and analyze the usefulness the weight vector along with its setting policies. This algorithm is consistent with the existing reduction algorithm based on discernibility in that the former contains the latter as a special case when all elements of the weight vector are equal and non-zero. Experiment results of the Bridges dataset in the UCI library validate the usefulness of our algorithm.