In this study, the classification problem is solved from the view of granular computing. That is, the classification problem is equivalently transformed into the fuzzy granular space to solve. Most classification algorithms are only adopted to handle numerical data; random fuzzy granular decision tree (RFGDT) can handle not only numerical data but also nonnumerical data like information granules. Measures can be taken in four ways as follows. First, an adaptive global random clustering (AGRC) algorithm is proposed, which can adaptively find the optimal cluster centers and maximize the ratio of interclass standard deviation to intraclass standard deviation, and avoid falling into local optimal solution; second, on the basis of AGRC, a parallel model is designed for fuzzy granulation of data to construct granular space, which can greatly enhance the efficiency compared with serial granulation of data; third, in the fuzzy granular space, we design RFGDT to classify the fuzzy granules, which can select important features as tree nodes based on information gain ratio and avoid the problem of overfitting based on the pruning algorithm proposed. Finally, we employ the dataset from UC Irvine Machine Learning Repository for verification. Theory and experimental results prove that RFGDT has high efficiency and accuracy and is robust in solving classification problems.

Rough sets have been widely used in the fields of machine learning and feature selection. However, the classical rough sets have the problems of difficultly dealing with real-value data and weakly fault tolerance. In this paper, by introducing a neighborhood rough set model, the values of decision systems are granulated into some condition and decision neighborhood granules. A concept of neighborhood granular swarm is defined in a decision system. Then the sizes of a neighborhood granule and a neighborhood granular swarm are also given. In order to enhance the fault-tolerant ability of classification systems, we define some concepts of granule inclusion, variable precision neighborhood approximation sets and positive region. We propose a variable precision neighborhood rough set model, and analyze its property. Furthermore, based on the positive region of a variable precision neighborhood, we give the significance of an attribute and use it to select feature subsets. A feature subset selection algorithm to the variable precision neighborhood rough sets is designed. Finally, the feature selection algorithm is carried out on the UCI datasets, and the selected features are tested by the SVM classification algorithm. Theoretical analysis and experiments show that the proposed method can find the effective and compact feature subsets, which have abilities of fault tolerance.

Linear regression is the use of linear functions to model the relationship between a dependent variable and one or more independent variables. Linear regression models have been widely used in various fields such as finance, industry, and medicine. To address the problem that the traditional linear regression model is difficult to handle uncertain data, we propose a granule-based elastic network regression model. First we construct granules and granular vectors by granulation methods. Then, we define multiple granular operation rules so that the model can effectively handle uncertain data. Further, the granular norm and the granular vector norm are defined to design the granular loss function and construct the granular elastic network regression model. After that, we conduct the derivative of the granular loss function and design the granular elastic network gradient descent optimization algorithm. Finally, we performed experiments on the UCI datasets to verify the validity of the granular elasticity network. We found that the granular elasticity network has the advantage of good fit compared with the traditional linear regression model.