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# Complex-valued Renyi Entropy

## Abstracts

 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.
From: 邓勇
DOI：10.12074/202106.00005
Recommended references： Lipeng Pan,Yong Deng.(2021).Complex-valued Renyi Entropy.[ChinaXiv:202106.00005] (Click&Copy)
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