Knowledge Reduction in Inconsistent Decision Tables

In this paper, we introduce a new type of reducts called the λ-Fuzzy-Reduct, where the fuzzy similarity relation is constructed by means of cosine-distances of decision vectors and the parameter λ is used to tune the similarity precision level. The λ-Fuzzy-Reduct can eliminate harsh requirements of the distribution reduct, and it is more flexible than the maximum distribution reduct, the traditional reduct, and the generalized decision reduct. Furthermore, we prove that the distribution reduct, the maximum distribution reduct, and the generalized decision reduct can be converted into the traditional reduct. Thus in practice the implementations of knowledge reductions for the three types of reducts can be unified into efficient heuristic algorithms for the traditional reduct. We illustrate concepts and methods proposed in this paper by an example.