For heterogeneous data sets containing numerical and symbolic feature values, feature selection based on fuzzy neighborhood multigranulation rough sets (FNMRS) is a very significant step to preprocess data and improve its classification performance. This article presents an FNMRS-based feature selection approach in neighborhood decision systems. First, some concepts of fuzzy neighborhood rough sets and neighborhood multigranulation rough sets are given, and then the FNMRS model is investigated to construct uncertainty measures. Second, the optimistic and pessimistic FNMRS models are built by using fuzzy neighborhood multigranulation lower and upper approximations from algebra view, and some fuzzy neighborhood entropy-based uncertainty measures are developed in information view. Inspired by both algebra and information views based on the FNMRS model, the fuzzy neighborhood pessimistic multigranulation entropy is proposed. Third, the Fisher score model is utilized to delete irrelevant features to decrease the complexity of high-dimensional data sets, and then, a forward feature selection algorithm is provided to promote the performance of heterogeneous data classification. Experimental results on 12 data sets show that the presented model is effective for selecting important features with the higher stability of classification in neighborhood decision systems.

Attribute reduction is one of the biggest challenges encountered in computational intelligence, data mining, pattern recognition and machine learning. Effective in feature selection as the rough set theory is, it can only handle symbolic attributes. In order to overcome this drawback, proposed is the fuzzy rough sets, an extended model of rough sets, which is able to deal with imprecision and uncertainty in both symbolic and numerical attributes. Existing attribute selection algorithms based on fuzzy rough set model mainly take the angle of “attribute set”, which means they define the object function representing the predictive ability for attributes subset with regard to the domain of discourse, rather than follow the view of “object pair”. Algorithms based on the latter can ignore the object pairs that are already discerned by the selected attributes subsets and thus need only to deal with part of object pairs instead of the whole object pairs from the discourse, which makes such algorithms more efficient in attribute selection. In this paper, we propose the concept of Reduced Maximal Discernibility Pair, which directly adopts the perspective of object pair in the framework of fuzzy rough set model. Then we develop two attribute selection algorithms, named as Reduced Maximal Discernibility Pair Selection (RMDPS) and Weighted Reduced Maximal Discernibility Pair Selection (WRMDPS), based on the reduced maximal discernibility pair. Experiment results show that the proposed algorithms are effective and efficient in attribute selection.

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.

Recently, multilabel classification has generated considerable research interest. However, the high dimensionality of multilabel data incurs high costs; moreover, in many real applications, a number of labels of training samples are randomly missed. Thus, multilabel classification can have great complexity and ambiguity, which means some feature selection methods exhibit poor robustness and yield low prediction accuracy. To solve these issues, this article presents a novel feature selection method based on multilabel fuzzy neighborhood rough sets (MFNRS) and maximum relevance minimum redundancy (MRMR) that can be used on multilabel data with missing labels. First, to handle multilabel data with missing labels, a relation coefficient of samples, label complement matrix, and label-specific feature matrix are constructed and implemented in a linear regression model to recover missing labels. Second, the margin-based fuzzy neighborhood radius, fuzzy neighborhood similarity relationship, and fuzzy neighborhood information granule are developed. The MFNRS model is built based on multilabel neighborhood rough sets combined with fuzzy neighborhood rough sets. Based on algebra and information views, certain fuzzy neighborhood entropy-based uncertainty measures are proposed for MFNRS. The fuzzy neighborhood mutual information-based MRMR model with label correlation is improved to evaluate the performance of candidate features. Finally, a feature selection algorithm is designed to improve the performance for multilabel data with missing labels. Experiments on 20 datasets verify that our method is effective not only for recovering missing labels but also for selecting significant features with better classification performance.