Approaches to Knowledge Reduction of Decision Systems based on Conditional Rough Entropy

Knowledge reduction in rough set theory is an important feature selection method. Since it is an NP-hard problem, it is necessary to investigate fast and effective approximate algorithms. In this paper, to address this issue, by introducing rough entropy in information systems, the novel measures of conditional rough entropy with distinguishing consistent objects form inconsistent objects are presented for both consistent and inconsistent decision systems. Thus, many important propositions, properties, and conclusions for reduct are drawn, and by using decomposition, radix sorting, hash, and input sequence techniques, we construct a forward greedy algorithm for knowledge reduction. Finally, through analyzing the given example, compared with some standard UCI datasets and other knowledge reduction algorithms, the proposed technique is effective and suitable for both consistent and inconsistent decision systems. Thus, it establishes the theoretical basis for seeking efficient algorithm of knowledge acquisition in decision systems.