Deng entropy: a generalized Shannon entropy to measure uncertainty

Shannnon entropy is an efficient tool to measure uncertain information. However, it cannot handle the more uncertain situation when the uncertainty is represented by basic probability assignment (BPA), instead of probability distribution, under the framework of Dempster Shafer evidence theory. To address this issue, a new entropy, named as Deng entropy, is proposed. The proposed Deng entropy is the generalization of Shannnon entropy. If uncertain information is represented by probability distribution, the uncertain degree measured by Deng entropy is the same as that of Shannnon’s entropy. Some numerical examples are illustrated to shown the efficiency of Deng entropy.