Fractals are important in science, and their dimension is crucial for understanding them. While existing methods can find the dimension of probability distributions, determining the dimension of mass functions, a more general concept, has been a challenge. This work introduces a new way to calculate the fractal dimension of mass functions. The researchers found that the dimension of a mass function with the highest Deng entropy is approximately 1.585, which is the well-known dimension of the Sierpiński triangle.