Fractal-based belief entropy

The total uncertainty measurement of basic probability assignment (BPA) in evidence theory has always been an open issue. Although many scholars have put forward various measures and requirements of bodies of evidence (BoE), none of them are widely recognized. So in order to express the uncertainty in evidence theory, transforming basic probability assignment (BPA) into probability distribution is a widely used method, but all the previous methods of probability transformation are directly allocating focal elements in evidence theory to their elements without specific transformation process. Based on above, this paper simulates the pignistic probability transformation (PPT) process based on the idea of fractal, making the PPT process and the information volume lost during transformation more intuitive. Then apply this idea to the total uncertainty measure in evidence theory. A new belief entropy called Fractal-based (FB) entropy is proposed, which is the first time to apply fractal idea in belief entropy. After verification, the new entropy is superior to all existing total uncertainty measurements.