Feature selection algorithm using neighborhood equivalence tolerance relation for incomplete decision systems

Rough set is an important method for dealing with incomplete information systems. In incomplete information systems, the most common way to determine the relation between two samples is the tolerance relation. However, the condition for the tolerance relation to determine those samples may belong to the same category is very lenient, which makes the reduction rate low when using the rough set generated by this relation to select features. In response to the above problems, we design the neighborhood equivalence tolerance relation to solve them. Different from other improved tolerance relations, firstly, the relation designed in this paper does not require additional threshold to accomplish the above goals, which will avoid the trouble caused by the given threshold. Secondly, we notice that most of the current improvements for this kind of problems are computationally cumbersome, and the relation designed in this paper is simple and effective. Based on this, we construct a neighborhood rough set model that handles incomplete information by using this relation, introduce its properties, expound the properties that a reduction set should satisfy, quantify the importance of conditional attributes with attribute dependence degree, which provides the basis for the design of feature selection algorithm. Finally, the greedy strategy is used to design a forward feature selection algorithm. Experimental results show that the model is effective in dealing with incomplete information systems. The feature selection algorithm has the smallest size of the average reduced subset on twelve datasets, and maintains the accuracy of the classifier, which verifies that the feature selection algorithm can effectively deal with incomplete information systems.