  The total uncertainty measurement of basic probability assignment (BPA) in
Dempster-Shafer evidence theory (DSET) has always been an open issue. Although
some scholars put forward various measurements and entropies of BPA, due to the
existence of discord and non-specificity, there is no method can measure BPA
reasonably. In order to utilize BPA to practical decision-making, pignistic
probability transformation of BPA is a significant method. In the paper, we
simulate the pignistic probability transformation (PPT) process based on the
fractal idea, which describes PPT process in detail and shows the process of
information volume changes during transformation intuitively. Based on
transformation process, we propose a new belief entropy called fractal-based
belief (FB) entropy. After verification, FB entropy is superior to all existing
belief entropies in terms of total uncertainty measurement and physical model
consistency.
