Soft-neighborhood based robust fuzzy rough sets for semi-supervised feature selection

Fuzzy rough set (FRS) theory has been widely concerned because of its successful application in dimensionality reduction of data. To reduce the sensitivity of the theory to noise and data distribution in practical applications, the study of robust FRS model still attracts great attention. This research is devoted to the robust fuzzy rough uncertainty measure theory for multi-density data. Firstly, soft-neighborhood theory is combined with classical FRSs to design a generalized FRS model which is simply named SNFRS. The new model can effectively reduce the influence of noise and multi-density distribution on uncertainty measure of data. Secondly, with the SNFRS model, soft fuzzy rough indiscernibility theory is proposed, and it is used to design feature selection algorithms. In this research, a fully supervised feature selection and a semi-supervised feature selection algorithms are respectively proposed based on the soft fuzzy rough indiscernibility theory. Besides, the labeling method of the semi-supervised feature selection is also based on the theory. Finally, some experiments are performed to verify the proposed models and algorithms. The results show that the feature selection algorithms based on the soft fuzzy rough indiscernibility are feasible and efficient. This indirectly indicates that the FRS model based on soft-neighborhood is effective, successful and generalized in measuring uncertainty of data.