Minkowski–Bouligand dimension

Statistics

Entropy (arrow of time)

Correlation dimension

Combinatorics

Effective dimension

Physics

Statistical physics

Multifractal system

Mathematical analysis

Probability distribution

Fractal analysis

Generalization

Hausdorff dimension

Probability mass function

Fractal dimension

Dimension function

Dimension (graph theory)

Mathematics

Fractal

Fractal dimension on networks

Quantum mechanics

Fractal derivative

Fractal landscape

Fractals

Fractal plays an important role in nonlinear science. The most important parameter to model fractal is fractal dimension. Existing information dimension can calculate the dimension of probability distribution. However, given a mass function which is the generalization of probability distribution, how to determine its fractal dimension is still an open problem of immense interest. The main contribution of this work is to propose an information fractal dimension of mass function. Numerical examples are illustrated to show the effectiveness of our proposed dimension. We discover an important property in that the dimension of mass function with the maximum Deng entropy is $\frac{ln3}{ln2}\approx 1.585$, which is the well-known fractal dimension of Sierpi\'nski triangle.

INFORMATION FRACTAL DIMENSION OF MASS FUNCTION