In the view of granular computing, some general uncertainty measures are proposed through single-granulation by generalizing Shannon’s entropy. However, in the practical environment we need to describe concurrently a target concept through multiple binary relations. In this paper, we extend the classical information entropy model to a multi-granulation entropy model (MGE) by using a series of general binary relations. Two types of MGE are discussed. Moreover, a number of theorems are obtained. It can be concluded that the single-granulation entropy is the special instance of MGE. We employ the proposed model to evaluate the significance of the attributes for classification. A forward greedy search algorithm for feature selection is constructed. The experimental results show that the proposed method presents an effective solution for feature analysis.

Preference mining plays an important role in e-commerce and video websites for enhancing user satisfaction and loyalty. Some classical methods are not available for the cold-start problem when the user or the item is new. In this paper, we propose a new model, called parametric neighborhood rough set on two universes (NRSTU), to describe the user and item data structures. Furthermore, the neighborhood lower approximation operator is used for defining the preference rules. Then, we provide the means for recommending items to users by using these rules. Finally, we give an experimental example to show the details of NRSTU-based preference mining for cold-start problem. The parameters of the model are also discussed. The experimental results show that the proposed method presents an effective solution for preference mining. In particular, NRSTU improves the recommendation accuracy by about 19% compared to the traditional method.

Rough set theory has been successfully applied to many fields, such as data mining, pattern recognition, and machine learning. Kernel rough sets and neighborhood rough sets are two important models that differ in terms of granulation. The kernel rough sets model, which has fuzziness, is susceptible to noise in the decision system. The neighborhood rough sets model can handle noisy data well but cannot describe the fuzziness of the samples. In this study, we define a novel model called kernel neighborhood rough sets, which integrates the advantages of the neighborhood and kernel models. Moreover, the model is used in the problem of feature selection. The proposed method is tested on the UCI datasets. The results show that our model outperforms classic models.