# Generalized Belief Function: A new concept for uncertainty modelling and processing

## TL;DR

This paper introduces a generalized belief function on the complex plane, extending Dempster-Shafer theory to better model and process uncertainty using complex numbers.

## Contribution

It proposes a novel complex mass function concept that generalizes traditional belief functions, enabling complex-valued uncertainty modeling.

## Key findings

- Complex mass functions extend traditional belief functions.
- Generalized belief and plausibility functions reduce to classical ones in real case.
- Provides a new framework for uncertainty modeling with complex numbers.

## Abstract

In this paper, we generalize the belief function on complex plane from another point of view. We first propose a new concept of complex mass function based on the complex number, called complex basic belief assignment, which is a generalization of the traditional mass function in Dempster-Shafer evidence theory. On the basis of the de nition of complex mass function, the belief function and plausibility function are generalized. In particular, when the complex mass function is degenerated from complex numbers to real numbers, the generalized belief and plausibility functions degenerate into the traditional belief and plausibility functions in DSE theory, respectively.