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Complex-valued Rényi entropy

Author

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  • Lipeng Pan
  • Yong Deng

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.

Suggested Citation

  • Lipeng Pan & Yong Deng, 2024. "Complex-valued Rényi entropy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(3), pages 926-937, February.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:3:p:926-937
    DOI: 10.1080/03610926.2022.2094963
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