Attribute reductions based on δ-fusion condition entropy and harmonic similarity degree in interval-valued decision systems

This paper defines an improved similarity degree based on inclusion degree as well as advanced information system based on interval coverage and credibility, and thus an attribute reduction framework embodying 4×2 = 8 reduct algorithms is systematically constructed for application and optimization in interval-valued decision systems. Firstly, a harmonic similarity degree is constructed by introducing interval inclusion degree and harmonic average mechanism, which has better semantic interpretation and robustness. Secondly, interval credibility degree and coverage degree are defined for information fusion, and they are combined to propose a δ-fusion condition entropy. The improved condition entropy achieves the information reinforcement and integrity by dual quantization fusion of credibility and coverage, and it obtains measure development from granularity monotonicity to non-monotonicity. In addition, information and joint entropies are also constructed to obtain system equations. Furthermore, 8 reduct algorithms are designed by using attribute significance for heuristic searches. Finally, data experiments show that our five novel reduct algorithms are superior to the three contrast algorithms on classification performance, which also further verify the effectiveness of proposed similarity degree, information measures and attribute reductions.