A Fractal-Based Complex Belief Entropy for Uncertainty Measure in Complex Evidence Theory
本文提出一种基于分形的复杂信念熵，用于度量复杂证据理论中的不确定性，通过数值实验和实际应用验证其有效性。
Complex evidence theory (CET), an extension of the traditional D-S evidence theory, has garnered academic interest for its capacity to articulate uncertainty through complex basic belief assignment (CBBA) and to perform uncertainty reasoning using complex combination rules. Nonetheless, quantifying uncertainty within CET remains a subject of ongoing research. To enhance decision making, a method for complex pignistic belief transformation (CPBT) has been introduced, which allocates CBBAs of multielement focal elements to subsets. CPBT’s core lies in the fractal-inspired redistribution of the complex mass function. This article presents an experimental simulation and analysis of CPBT’s generation process along the temporal dimension, rooted in fractal theory. Subsequently, a novel fractal-based complex belief (FCB) entropy is proposed to gauge the uncertainty of CBBA. The properties of FCB entropy are examined, and its efficacy is demonstrated through various numerical examples and practical application.