Complex Deng entropy for uncertainty measure in complex evidence theory

Dempster–Shafer (DS) evidence theory, an extension of probability theory, is widely utilized across various domains due to its adeptness in managing uncertain and imprecise information. Building on DS evidence theory, the complex evidence theory addresses uncertainty in decision-making in a complex plane framework. Uncertainty measurement holds a pivotal role in both evidence theory and probability theory. In this paper, capitalizing on the unique attributes of complex basic belief assignment (CBBA), we propose a novel measure of complex belief entropy, designed to evaluate total uncertainty in complex evidence theory. Notably, the proposed complex belief entropy encompasses not only discord and non-specificity but also interference, shedding light on the interactions among focal elements. Additionally, we conduct a thorough analysis of the properties associated with this newly proposed entropy. Finally, based on the proposed entropy model, a decision-making algorithm is proposed, demonstrating the superiority of the entropy model. Our findings reveal that the proposed complex belief entropy effectively measures the total uncertainty of CBBA in the framework of complex evidence theory.