Abstract: New feature subset selection algorithms arc presented in this paper to reduce the heavy computational load of available algorithms to feature subset selection for incomplete decision systems. We firstly propose the
forward sequential feature selection algorithm for incomplete decision systems based on the fact that that the discernibility of an incomplete decision system will not change with its unchangeable positive region; then we
generalize the algorithm to heterogeneous incomplete decision systems based on neighborhood rough sets theory;finally we extend the fast approach to attribute reduction in incomplete decision systems with tolerance relation-based
rough sets to the heterogeneous incomplete decision systems based on neighborhood rough sets theory to accomplish the feature subset selection procedure for incomplete decision systems with quantity or heterogeneous attributes. We
rank features (attributes) in descending order according to their significance to positive region, then select the top one feature from current feature subset and add it to the reduction of attributes, whilst delete it from current feature
subset，where the attribute reduction subset is empty at first, while current feature subset is initialized with all features. Theoretical analysis and experimental results on datasets from University of California lrvinc(UCl)
machine learning repository demonstrate that our forward sequential feature subset selection algorithms for incomplete decision systems based on neighborhood rough sets arc more efficient than the backward feature subset
selection algorithms. The potential disadvantage of our forward sequential feature subset selection algorithms is that the feature subset selection procedure may not be completed for the first important feature cannot be found at the first iteration.