Higher order information volume of mass function

TL;DR

This paper introduces the higher order information volume of mass function by generalizing Deng entropy through a fractal-based approach, enabling better prediction of uncertainty over time.

Contribution

It provides a new fractal-based explanation for Deng entropy and proposes TFB entropy, capturing more uncertain information than existing methods.

Findings

Introduces TFB entropy as a generalization of Deng entropy.

Defines higher order information volume of mass function (HOIVMF).

Demonstrates TFB entropy's ability to predict uncertainty over time.

Abstract

For a certain moment, the information volume represented in a probability space can be accurately measured by Shannon entropy. But in real life, the results of things usually change over time, and the prediction of the information volume contained in the future is still an open question. Deng entropy proposed by Deng in recent years is widely applied on measuring the uncertainty, but its physical explanation is controversial. In this paper, we give Deng entropy a new explanation based on the fractal idea, and proposed its generalization called time fractal-based (TFB) entropy. The TFB entropy is recognized as predicting the uncertainty over a period of time by splitting times, and its maximum value, called higher order information volume of mass function (HOIVMF), can express more uncertain information than all of existing methods.