Complex-valued Rényi entropy

Abstract

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 information. Therefore, how to reasonably measure the uncertain information of the complex-valued information is a gap to be filled. In this paper, inspired by the Rényi entropy, we propose the complex-valued Rényi entropy, which measures uncertain information of the complex-valued probability under the framework of complex number, and this is also the first time to measure uncertain information in the complex space. The complex-valued Rényi entropy contains the features of the classical Rényi entropy, i.e., the complex-valued Rényi entropy corresponds to different information functions with different parameters q. Moreover, complex-valued Rényi entropy has some properties, such as non-negativity, monotonicity and etc. Some numerical examples can demonstrate the flexibility and reasonableness of the complex-valued Rényi entropy.

Keywords:

• Complex-valued probability
• Rényi entropy
• complex-valued Rényi entropy
• uncertain information

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Funding

The authors greatly appreciate the reviews’ suggestions and the editor’s encouragement. The work is partially supported by National Natural Science Foundation of China (Grant No. 61973332), JSPS Invitational Fellowships for Research in Japan (Short-term).