Multifractal of mass function

TL;DR

This paper introduces a multifractal framework for mass functions, extending multifractal analysis to better handle uncertain information, with definitions, properties, and numerical illustrations.

Contribution

It proposes the concept of multifractal spectrum and dimension for mass functions, extending existing multifractal analysis to uncertain information models.

Findings

Multifractal dimension with maximum Deng entropy is 1.585.

The multifractal dimension reduces to Renyi's information dimension for probability distributions.

Numerical examples illustrate the properties of the proposed model.

Abstract

Multifractal plays an important role in many fields. However, there is few attentions about mass function, which can better deal with uncertain information than probability. In this paper, we proposed multifractal of mass function. Firstly, the definition of multifractal spectrum of mass function is given. Secondly, the multifractal dimension of mass function is defined as $D_{\alpha}$. When mass function degenerates to probability distribution, $D_{\alpha}$ degenerates to $d_{\alpha}$, which is information dimension proposed by Renyi. One interesting property is that the multifractal dimension of mass function with maximum Deng entropy is 1.585 no matter the order. Other interesting properties and numerical examples are shown to illustrate proposed model.