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Multifractal analysis of mass function.

Chenhui Qiang1,2, Zhen Li3, Yong Deng4

  • 1Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, 610054 China.

Soft Computing
|June 26, 2023
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Summary
This summary is machine-generated.

This study introduces a generalized multifractal dimension for mass functions in Dempster-Shafer theory, enhancing scale invariance and improving classification accuracy in evidence-based systems.

Keywords:
Cantor setDeng entropyDimensionMass functionMultifractalRenyi entropy

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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.