INFORMATION VOLUME FRACTAL DIMENSION

Abstract

There has been immense interest in uncertainty measurement because most real-world problems are accompanied by uncertain events. Therefore, Deng entropy has been proposed to measure the uncertainty in the probability theory and evidence theory. In this paper, we show that the uncertainty of the basic probability assignment (BPA) separated through the maximum Deng entropy separation rule (MDESR) is larger than the maximum Deng entropy of the original BPA. In addition, when the cardinality of the frame of discernment increases, the maximum information volume becomes larger and converges slower. The information volume fractal dimension is then proposed to describe the fractal property of uncertainty about the separated BPA distribution, which indicates the inherent physical meanings of Deng entropy from the perspective of statistics. This work can inspire further research on the fractal property of Deng entropy. Some experiments are applied to show the applicability of our proposed information volume fractal dimension.