Current Location:home > Browse

## 1. chinaXiv:202106.00009 [pdf]

Subjects: Computer Science >> Other Disciplines of Computer Science

 Complex evidence theory has been applied to several fields due to its advantages in modeling and processing uncertain information. However,to measure the uncertainty of the complex mass function is still an open issue. The main contribution of this paper is to propose a complex-valued Deng entropy. The complex-valued Deng entropy can effectively measure the uncertainty of the mass function in the complex-valued framework. Meanwhile, the complex-valued Deng entropy is a generalization of the Deng entropy and Shannon entropy. That is, the complex-valued Deng entropy can degenerate to classical Deng entropy when the complex-valued mass function degenerates to a mass function in real space. In addition, the proposed complex-valued Deng entropy can also degenerates to Shannon entropy when the complex-valued mass function degenerates to a probability distribution in real space. Some numerical examples demonstrate the compatibility and effectiveness of the complex-valued Deng entropy.

## 2. chinaXiv:202106.00005 [pdf]

Subjects: Computer Science >> Other Disciplines of Computer Science

 Complex-valued expression models have been widely used in the application of intelligent decision systems. However, there is a lack of entropy to measure the uncertain information of the complex-valued probability distribution. Therefore, how to reasonably measure the uncertain information of the complex-valued probability distribution is a gap to be filled. In this paper, inspired by the Renyi entropy, we propose the Complex-valued Renyi entropy, which can measure uncertain information of the complex-valued probability distribution under the framework of complex numbers, and is also the first time to measure uncertain information in the complex space. The Complex-valued Renyi entropy contains the features of the classical Renyi entropy, i.e., the Complex-valued Renyi Entropy corresponds to different information functions with different parameters q. Meanwhile, the Complex-valued Renyi entropy has some properties, such as non-negativity, monotonicity, etc. Some numerical examples can demonstrate the flexibilities and reasonableness of the Complex-valued Renyi entropy.