Feature selection using three-stage heuristic measures based on mutual fuzzy granularities

Mutual information is fundamental for feature selection, and relevant conditional and joint mutual fuzzy granularities (MFGs) characterize feature correlation and redundancy in fuzzy decision systems, respectively. Recently, conditional MFGs have been utilized to generate three-stage heuristic measures, and thus, two feature selection algorithms (called GFMRI-FS and NGFMRI-FS) have emerged. However, these methods emphasize correlation connections but neglect redundancy deletion, thus the approach can be improved. In this paper, a joint MFG with redundant feature information is supplemented to reasonably modify existing heuristic measures, and new three-stage heuristic measures are constructed to obtain two improved selection algorithms (called C-GFMRI-FS and C-NGFMRI-FS). First, the measurement mechanisms of the MFGs are analyzed, and three-stage correctional heuristic measures are established to acquire the dependency semantics, bound combinations, size relationships, theoretical extensions, applied optimization, parametric monotonicity, and systematic algorithms. Then, the three-stage current and correctional heuristic measures obtain granulation monotonicity/certainty and nonmonotonicity/uncertainty, respectively, as well as uncertainty fluctuations on feature-dynamic subset chains. Furthermore, feature selection is investigated by correctional heuristic measures, and two selection algorithms (i.e., C-GFMRI-FS and C-NGFMRI-FS) are designed. Finally, table examples and data experiments validate the uncertainty heuristic measures and feature selection algorithms; accordingly, C-GFMRI-FS and C-NGFMRI-FS outperform GFMRI-FS and NGFMRI-FS and achieve better classification results. This study fuses conditional and joint MFGs to make systematic improvements in heuristic measurements and feature selection, thus facilitating data learning.