A New Complex Deng Entropy with Its Application in Pattern Classification

Complex evidence theory is an effective method for modeling and reasoning uncertain information. But how to handle and measure the uncertainty of complex basic belief assignments is still an open issue. The meaning of this paper is to propose a new complex Deng entropy in complex evidence theory including the information on phase angle and measure of discord and non-specificity. It effectively expresses the uncertainty of complex basic belief assignments and considers more phase information, that is, the physical meaning of the phase angle. When the phase is zero, the number degenerates into a real number, and the new complex Deng entropy degenerates into Deng entropy. And Deng entropy degenerates to Shannon entropy when the space is assumed to be a single subset. We give some numerical examples and discuss them to study the compatibility and effectiveness of the new complex Deng entropy. At last, we apply the proposed new complex Deng entropy to pattern classification. The results further verify that the new complex Deng entropy has better recognition accuracy than the complex-valued Deng entropy on some data sets.