A fractal-based supremum and infimum complex belief entropy in complex evidence theory

Complex evidence theory is a generalized Dempster–Shafer evidence theory, which has the ability to express uncertain information. One of the key issues is the uncertainty measure of Complex Basic Belief Assignment (CBBA). However, the research on the uncertainty measure of complex evidence theory is still an open issue. Therefore, in this paper, first, the Fractal-based Complex Belief (FCB) entropy as a generalization of Fractal-based Belief (FB) entropy, which has superiority in uncertainty measurement of CBBA, is proposed. Second, on the basis of FCB entropy, we propose Fractal-based Supremum Complex Belief (FSCB) entropy and Fractal-based Infimum Complex Belief (FICB) entropy, with FSCB entropy as the upper bound and FICB entropy as the lower bound. They are collectively called the proposed FCB entropy. Furthermore, we analyze the properties, physical interpretation and numerical examples to prove the rationality of the proposed method. Finally, a practical information fusion application is proposed to prove that the proposed FCB entropy can reasonably measure the uncertainty of CBBA. The results show that, the proposed FCB entropy can handle the uncertainty measure of CBBA, which can be a reasonable way for uncertainty measure in complex evidence theory.