Abstract
In fuzzy neighborhood rough sets (FNRSs), uncertainty measurement performs mainly classification-hierarchical and multiplication-simple fusion, so the corresponding feature selection has advancement space. This paper aims to improve uncertainty measurement and feature selection via FNRSs. Two measurement strategies regarding class-hierarchical fusion and multiplication-optimal fusion are proposed, and three measure-based heuristic feature selection algorithms are developed. Concretely, fuzzy neighborhood self-information (FNSI) and joint entropy (FNJE) constitute two bases of heterogeneous fusion, and their multiplication fusion induces both the existing measure FNSIJE (which is based on classification-level fusion) and a new measure CFNSIJE (which is based on class-level fusion); furthermore, FNSIJE and CFNSIJE are extended to the optimal measures FNSIJEE and CFNSIJEE, respectively, by exponential parameterization. The four types of fusion measures acquire their calculation algorithms and granulation nonmonotonicity and systematically motivate four heuristic feature selection algorithms, i.e., the current FNSIJE-FS and the new CFNSIJE-FS, FNSIJEE-FS, and CFNSIJEE-FS. By using examples and experiments, relevant uncertainty measurement and granulation nonmonotonicity are validated, while the novel selection algorithms demonstrate better classification performances. This study establishes the hierarchical fusion and exponential expansion to acquire robust uncertainty measurement and optimal feature selection, and the measurement, nonmonotonicity, and selection have strong generalization for information fusion and rough-set learning.
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