Attribute selection based on a new conditional entropy for incomplete decision systems

Shannon’s entropy and its variants have been applied to measure uncertainty in rough set theory from the viewpoint of information theory. However, few studies have been done on attribute selection in incomplete decision systems based on information-theoretical measurement of attribute importance. In this paper, we introduce a new form of conditional entropy to measure the importance of attributes in incomplete decision systems. Based on the introduced conditional entropy, we construct three attribute selection approaches, including an exhaustive search strategy approach, a greedy (heuristic) search strategy approach and a probabilistic search approach for incomplete decision systems. To test the effectiveness of these methods, experiments on several real-life incomplete data sets are conducted. The results indicate that two of these methods are effective for attribute selection in incomplete decision system.