Feature selections based on three improved condition entropies and one new similarity degree in interval-valued decision systems

Feature selections facilitate classification learning in various data environments. Aiming at interval-valued decision systems (IVDSs), feature selections rely on information measures and similarity degrees, whereas current selection algorithms on credibility-based condition entropy and classical similarity degree are accompanied with some measurement limitations and advancement space. In this paper based on IVDSs, three coverage-credibility-based condition entropies and one geometry-probabilistic similarity degree are proposed across two dimensions of informationization and granulation, and they improve the existing condition entropy and similarity degree; accordingly, 4 x 2 feature selections emerge for optimization and applicability, and they systematically contain one initial selection algorithm and seven new/robuster algorithms. At first, three-way granular measures (i.e., credibility, coverage, and integrated coverage-credibility) are formulated in IVDSs, and three novel condition entropies are established by implementing three information structures on coverage-credibility. These condition entropies acquire in-depth improvements, hierarchical algorithms, size relationships, maximum/minimum conditions, and granulation non-monotonicity. Then, the probabilistic similarity degree is defined by a six-piecewise function with quadratic factors, and this new measure gains the geometry-probability mechanism and high-quality improvement. Furthermore, feature selections are determined by preserving condition entropies and by mining feature significances, so eight selection algorithms are obtained by combining condition entropies and similarity degrees. Finally, data experiments are performed to validate relevant uncertainty measures and feature selections, and seven constructional selection algorithms outperform three contrastive algorithms to achieve better classification performances.