The concept of dependency in a neighborhood rough set model is an important evaluation function for the feature selection. This function considers only the classification information contained in the lower approximation of the decision while ignoring the upper approximation. In this paper, we construct a class of uncertainty measures: decision self-information for the feature selection. These measures take into account the uncertainty information in the lower and the upper approximations. The relationships between these measures and their properties are discussed in detail. It is proven that the fourth measure, called relative neighborhood self-information, is better for feature selection than the other measures, because not only does it consider both the lower and the upper approximations but also the change of its magnitude is largest with the variation of feature subsets. This helps to facilitate the selection of optimal feature subsets. Finally, a greedy algorithm for feature selection has been designed and a series of numerical experiments was carried out to verify the effectiveness of the proposed algorithm. The experimental results show that the proposed algorithm often chooses fewer features and improves the classification accuracy in most cases.

A fuzzy rough set is an important rough set model used for feature selection. It uses the fuzzy rough dependency as a criterion for feature selection. However, this model can merely maintain a maximal dependency function. It does not fit a given dataset well and cannot ideally describe the differences in sample classification. Therefore, in this study, we introduce a new model for handling this problem. First, we define the fuzzy decision of a sample using the concept of fuzzy neighborhood. Then, a parameterized fuzzy relation is introduced to characterize the fuzzy information granules, using which the fuzzy lower and upper approximations of a decision are reconstructed and a new fuzzy rough set model is introduced. This can guarantee that the membership degree of a sample to its own category reaches the maximal value. Furthermore, this approach can fit a given dataset and effectively prevents samples from being misclassified. Finally, we define the significance measure of a candidate attribute and design a greedy forward algorithm for feature selection. Twelve datasets selected from public data sources are used to compare the proposed algorithm with certain existing algorithms, and the experimental results show that the proposed reduction algorithm is more effective than classical fuzzy rough sets, especially for those datasets for which different categories exhibit a large degree of overlap.

Classical rough set theory is considered as a useful tool for dealing with the uncertainty of categorical data; the major deficiency of this model is that the classical rough set model is sensitive to noise in classification learning due to the stringent condition of equivalence relation. Thus, a class of fuzzy similarity relations was introduced to describe the similarity between samples with categorical attributes. However, these kinds of similarity relations also have deficiencies when they are used in fuzzy rough computation. In this paper, we propose a new fuzzy-rough-set model for categorical data by introducing a variable parameter to control the similarity of samples. This model employs the iterative computation strategy to define fuzzy rough approximations and dependency functions. It is proved that the proposed rough dependency function is monotonic. Finally, the proposed model is applied to the attribute reduction of categorical data. The experimental results indicate that the proposed model is more effective for categorical data than some existing algorithms.

Fuzzy rough set approaches have received widespread attention across the disciplines of feature selection and rule extraction. When calculating the fuzzy degree of membership of a sample within a specific class, traditional fuzzy rough sets give precedence to the distance information between the sample and other samples that do not belong to the class, often neglecting the influence of the remoteness of the sample from the specified class. In fact, this calculation strategy limits the discriminability of different samples relative to a given class, which may affect the accuracy and efficiency of feature subset selection. To address the shortcoming, the present study puts forward a new fuzzy rough set approach, weighted fuzzy rough set, which can more accurately measure the correlation and difference between samples relative to the decision class. Based on the distance from a sample to a class, the model first defines the importance of the sample to the class and uses it as a weight to measure the distance between the sample and other samples that do not belong to the class, thereby constructing a more effective fuzzy rough approximation operator. On this basis, a dependency measure between decision variables and conditional attributes is defined to evaluate the importance of candidate features. Then, a concept of discrimination between samples relative to a class is proposed, and the rationality of weighted fuzzy rough set is discussed. Finally, based on weighted fuzzy rough approximation operator, a new algorithm for selecting a subset of features is formulated. Experimental outcomes demonstrate that the algorithm performs well in terms of performance, not only selecting a smaller number of features, but also achieving higher classification accuracy for simplified data, showing its practical application value in feature selection.