# Evidential distance measure in complex belief function theory

## TL;DR

This paper introduces a new evidential distance measure for complex belief functions, extending existing real-valued measures to the complex domain, enabling more general and nuanced comparison of evidences.

## Contribution

The paper proposes a novel distance measure for complex belief functions, generalizing existing real-valued measures and enabling more comprehensive evidence comparison in complex spaces.

## Key findings

- Distance reduces to Jousselme's when applied to real-valued belief assignments
- Provides a more general framework for measuring differences between complex evidences
- Enhances the capability to compare complex belief functions in various applications

## Abstract

In this paper, an evidential distance measure is proposed which can measure the difference or dissimilarity between complex basic belief assignments (CBBAs), in which the CBBAs are composed of complex numbers. When the CBBAs are degenerated from complex numbers to real numbers, i.e., BBAs, the proposed distance will degrade into the Jousselme et al.'s distance. Therefore, the proposed distance provides a promising way to measure the differences between evidences in a more general framework of complex plane space.