Systematic Feature Selection Based on Three-Level Improvements of Fuzzy Dominance Three-Way Neighborhood Rough Sets

Feature selection facilitates system processing, and it relies on knowledge granulation and uncertainty measurement. Focusing on ordered decision systems, the fuzzy dominance neighborhood (FDN) granulation and corresponding condition entropy have recently yielded an outstanding algorithm for feature selection, FDNCE-FS (fuzzy dominance neighborhood condition entropy-based feature selection). However, there is room for improvement. Accordingly, three-level improvements of knowledge granulation, information enrichment, and heterogeneity fusion are proposed here, and $2\times 2\times 2=8$ heuristic algorithms of feature selection are systematically established. First, FDN granulation is improved to fuzzy dominance three-way neighborhood (FD3N) granulation through three-way decision on fuzzy dominance degrees, and FD3N rough sets are modeled to offer better dependency. Second, the FDN condition entropy is improved to FD3N condition entropy by reinforcing the interaction factor and class information, and corresponding measure systems are constructed. Third, FD3N dependency is fused with four types of condition entropy to produce four combined measures, and eight uncertainty measures hierarchically emerge due to the three-level improvements. Fourth, these systematic measures have granulation nonmonotonicity, and they enable heuristic algorithms for feature selection; thus, the current FDNCE-FS method is improved to seven new selection algorithms: FHN-FS, RHN-FS, RFHN-FS, HTWN-FS, FHTWN-FS, RHTWN-FS, and RFHTWN-FS. Finally, the relevant FD3N granulation, uncertainty measurement, and feature selection are validated by data-based experiments, and the seven novel algorithms are shown to outperform FDNCE-FS in terms of classification performance. This study provides new insights into uncertainty modeling, information fusion, and feature selection through granular computing and three-way decision.