A Fractal-based Complex Belief Entropy for Uncertainty Measure in Complex Evidence Theory

TL;DR

This paper introduces a fractal-inspired complex belief entropy measure within Complex Evidence Theory to better quantify uncertainty, supported by simulations and practical examples.

Contribution

It proposes a novel fractal-based belief entropy for CET, enhancing uncertainty quantification with a new transformation and analysis method.

Findings

Fractal-based belief entropy effectively measures uncertainty in CET.

The method is validated through numerical examples and practical applications.

Abstract

Complex Evidence Theory (CET), an extension of the traditional D-S evidence theory, has garnered academic interest for its capacity to articulate uncertainty through Complex Basic Belief Assignment (CBBA) and to perform uncertainty reasoning using complex combination rules. Nonetheless, quantifying uncertainty within CET remains a subject of ongoing research. To enhance decision-making, a method for Complex Pignistic Belief Transformation (CPBT) has been introduced, which allocates CBBAs of multi-element focal elements to subsets. CPBT's core lies in the fractal-inspired redistribution of the complex mass function. This paper presents an experimental simulation and analysis of CPBT's generation process along the temporal dimension, rooted in fractal theory. Subsequently, a novel Fractal-Based Complex Belief (FCB) entropy is proposed to gauge the uncertainty of CBBA. The properties of FCB entropy are examined, and its efficacy is demonstrated through various numerical examples and practical application.