Multifractal analysis of mass function

Area of Science:

• Information Theory
• Artificial Intelligence
• Mathematical Analysis

Background:

• Dempster-Shafer evidence theory deals with uncertainty using mass functions.
• Existing fractal dimensions for mass functions lack compatibility with Renyi information dimensions.
• Scale invariance of belief entropy is a key characteristic to explore.

Purpose of the Study:

• To generalize the fractal dimension of mass functions by introducing a parameter.
• To propose a multifractal dimension for mass functions that incorporates scale invariance.
• To develop a method for improving classification accuracy using modified mass functions.

Main Methods:

• Introduction of a parameter to generalize existing fractal dimensions, creating a multifractal dimension.
• Exploration of the relationship between belief degree and focal elements using multifractal spectrum.
• Development of a static discounting coefficient method for mass function modification.

Main Results:

• The proposed multifractal dimension generalizes existing ones and shows compatibility with Renyi dimensions.
• The multifractal spectrum reveals relationships between belief degree and focal elements.
• The static discounting coefficient method effectively improves classification accuracy on three datasets.

Conclusions:

• The multifractal dimension of mass functions is a valuable tool for analyzing fractal characteristics in Dempster-Shafer theory.
• The proposed method offers a novel approach to enhance evidence classification accuracy.
• Further research can explore the applications of multifractal analysis in complex systems.