Faithful Approximations of Belief Functions

TL;DR

This paper develops a theoretical foundation for approximating belief functions, introduces heuristic methods for practical computation, and evaluates their accuracy and efficiency compared to previous approaches.

Contribution

It proposes a new conceptual framework for belief function approximation, analyzes the optimal solution's intractability, and introduces heuristic methods with experimental evaluation.

Findings

Heuristic methods are effective in approximating belief functions.

Optimal approximation is computationally intractable.

Heuristic methods outperform earlier approximations in speed and accuracy.

Abstract

A conceptual foundation for approximation of belief functions is proposed and investigated. It is based on the requirements of consistency and closeness. An optimal approximation is studied. Unfortunately, the computation of the optimal approximation turns out to be intractable. Hence, various heuristic methods are proposed and experimantally evaluated both in terms of their accuracy and in terms of the speed of computation. These methods are compared to the earlier proposed approximations of belief functions.