Complex-valued Renyi entropy

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 Renyi entropy, we propose the complex-valued Renyi 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 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. Moreover, complex-valued Renyi entropy has some properties, such as non-negativity, monotonicity and etc. Some numerical examples can demonstrate the flexibility and reasonableness of the complex-valued Renyi entropy.