Incomplete hybrid attributes reduction based on neighborhood granulation and approximation

There are two semantic explanations including the lost and the unrelated for the missing values. To deal with the hybrid information systems which including the numerical attributes and the missing value attributes, a generalized incomplete rough set model is proposed based on neighborhood relations. The model approximates an arbitrary subset in the universe with neighborhood granules, and the generalized neighborhood relations are the generalization of the asymmetry similarity relations and the tolerance relations. It overcomes the shortcoming that the classical rough set can not deal with numerical attributes directly and can deal with the generalized incomplete system which has the missing values both include the lost and the unrelated. The discrimination methods of the missing value and a hybrid reduction algorithm are proposed also. The discrimination methods of the lost or the unrelated conditions are proposed based on the assumption of the consistency classification, and the influence of the noise samples and the neighborhood values to the classification accuracy is presented as well. The validity and feasibility of the reduction algorithm are demonstrated by the results of experiments on five UCI machine learning databases.