Feature selections based on fuzzy probability dominance rough sets in interval-valued ordered decision systems

Feature selections (FSs) can greatly reduce the dimensionality and complexity of data, improving the efficiency of data mining and classification learning. For interval-valued ordered decision systems (IVODSs), FSs rely on dominance degrees and information measures; however, there are few selection algorithms based on fusion measurements and few semantic analyses of dominance degrees. Around IVODSs, this paper proposes fuzzy probability dominance rough sets (FPDRSs), an information measurement system and a fusion measure, and thus it constructs a systemic FSs framework. Firstly, we utilize a probability density function to propose the fuzzy probability dominance degree (FPD) that can deeply characterize the fuzzy probability dominance relation (FPDR) between any ordered interval values, and define fuzzy probability dominance dual approximations and dependency (FPDD), so FPDRSs are constructed. Then, the fuzzy probability dominance information entropy, conditional entropy (FPDCE), joint entropy and mutual information are obtained to constitute an information measurement system. Furthermore, a fuzzy probability dominance dependency-conditional entropy (FPDDCE) is defined. In addition, the monotonicity and nonmonotonicity of uncertainty measures are studied. Afterwards, three algorithms FPDD-FS, FPDCE-FS and FPDDCE-FS are constructed by using FPDD, FPDCE and FPDDCE, where attribute significance is used for heuristic searches. Finally, the effectiveness of the proposed uncertainty measures is verified through data experiments, and three proposed algorithms achieve better classification performance than six comparative algorithms.