A Comparison of Algorithms to Achieve the Maximum Entropy in the Theory of Evidence

TL;DR

This paper compares two algorithms for calculating maximum entropy in evidence theory, showing they are more similar in performance than previously thought.

Contribution

The study experimentally shows that the classical belief function algorithm can be more efficient than the reachable probability interval approach in certain cases.

Findings

The classical algorithm can be more efficient depending on the information representation.

Differences between the two algorithms are less pronounced than previously suggested.

Both algorithms yield similar maximum entropy values under specific conditions.

Abstract

Within the framework of evidence theory, maximum entropy is regarded as a measure of total uncertainty that satisfies a comprehensive set of mathematical properties and behavioral requirements. However, its practical applicability is severely questioned due to the high computational complexity of its calculation, which involves the manipulation of the power set of the frame of discernment. In the literature, attempts have been made to reduce this complexity by restricting the computation to singleton elements, leading to a formulation based on reachable probability intervals. Although this approach relies on a less specific representation of evidential information, it has been shown to provide an equivalent maximum entropy value under certain conditions. In this paper, we present an experimental comparative study of two algorithms for calculating maximum entropy in evidence theory: the classical algorithm, which operates directly on belief functions, and an alternative algorithm based on reachable probability intervals. Through numerical experiments, we demonstrate that the differences between these approaches are less pronounced than previously suggested in the literature. Depending on the type of information representations to which it is applied, the original algorithm based on belief functions can be more efficient than the one using the reachable probability interval approach. This is an interesting result, and a reason for choosing one algorithm over the other depending on the situation.