Implementing general belief function framework with a practical codification for low complexity

TL;DR

This paper introduces a practical, low-complexity codification for belief functions, simplifying manipulation of focal elements and decision processes within the framework, suitable for researchers and users.

Contribution

It presents a new codification method for belief functions that reduces complexity and integrates constraints from the start, along with decision approaches based on specificity.

Findings

Reduced hyper power set $D_r^\Theta$ simplifies belief function manipulation.

Two decision approaches are proposed: extension and specificity-based.

Practical coding methods are provided for belief function applications.

Abstract

In this chapter, we propose a new practical codification of the elements of the Venn diagram in order to easily manipulate the focal elements. In order to reduce the complexity, the eventual constraints must be integrated in the codification at the beginning. Hence, we only consider a reduced hyper power set $D_r^\Theta$ that can be $2^\Theta$ or $D^\Theta$. We describe all the steps of a general belief function framework. The step of decision is particularly studied, indeed, when we can decide on intersections of the singletons of the discernment space no actual decision functions are easily to use. Hence, two approaches are proposed, an extension of previous one and an approach based on the specificity of the elements on which to decide. The principal goal of this chapter is to provide practical codes of a general belief function framework for the researchers and users needing the belief function theory.