Feature Selection in High-Dimensional Set-Valued Decision System

In the decision system, the lower approximation set keeps expanding with adding features dynamically. But when enough features are added, the lower approximation set stabilizes. This provides a criterion for feature selection in high-dimensional decision set. Semi-monolayer covering rough set is an approximate representation of uncertain knowledge in set-valued decision system. This paper proposes a feature selection algorithm for high-dimensional set-valued decision system based on incremental update theory (abbr. SMCDA). Specifically, the trend of lower DA0 approximation set under the variation of features in the set-value information system is described, and the incremental limit of the lower DA0 approximation set is illustrated. The incremental algorithm of the lower DA0 approximation under the variation of features is designed. Next, the lower DA0 approximation set is continuously updated using the incremental algorithm until stable. At this point, the already added features are the result of feature selection for SMCDA. Experimental results show that the SMCDA algorithm has a good feature reduction effect.