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 multi-element focal elements to subsets. CPBT's core lies in the fractal-inspired redistribution of the complex mass function. This paper 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.

翻译：复杂证据理论（CET）作为传统D-S证据理论的扩展，因其通过复杂基本信念指派（CBBA）表达不确定性，并利用复杂组合规则进行不确定性推理的能力而受到学术界关注。然而，在CET中量化不确定性仍是一个持续研究的课题。为优化决策，一种复杂pignistic信念转换（CPBT）方法已被提出，该方法将多元素焦元的CBBAs分配至子集。CPBT的核心在于基于分形思想的复杂质量函数重分配。本文基于分形理论，沿时间维度对CPBT的生成过程进行了实验模拟与分析。随后，提出了一种新型的基于分形的复杂信念（FCB）熵，用于度量CBBA的不确定性。本文考察了FCB熵的性质，并通过多种数值算例及实际应用验证了其有效性。