An exponential negation of complex basic belief assignment in complex evidence theory

Negation is an important operation in evidence theory, whose idea is to consider the oppo-site of events, can deal with some problems with uncertainties from the opposite side and obtain information behind probability distribution. In classical D-S theory (Dempster-Shafer's theory), there are already many negation methods existed on real number field and many properties of which have been discovered. However, in complex evidence theory, which based on complex number field, negation is still an open problem. In order to deal with some problems like those in D-S theory, a new negation method for CBBA (Complex Basic Belief Assignment) should be proposed. In this paper, a new negation method called CBBA exponential negation will be presented, which can be seen as a generalization from BBA (Basic Belief Assignment) to CBBA. This proposed negation transforms a CBBA to another one with the entropy increased simultaneously. Also, some properties of this nega-tion will be discussed such as invariance, convergence, fixed point, distribution of Pascal triangle, convergence speed, impact on negation convergence and so on. Besides, most among them will be strictly proved in this paper. Furthermore, a new entropy for CBBA and some numerical examples will be presented, and we will study the proposed negation from the view of entropy. Finally, an application of CBBA exponential negation will be shown in the end.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

Negation is a crucial operation in evidence theory, but in complex evidence theory, which is based on complex number field, negation is still an open problem. Therefore, a new negation method called CBBA exponential negation is proposed and discussed in this paper. This method transforms a CBBA to another one with increased entropy. Various properties of this negation method are rigorously proved, and its impact on negation convergence is also studied. Additionally, a new entropy for CBBA and some numerical examples are presented, and an application of CBBA exponential negation is demonstrated.