Compatibility of Quantitative and Qualitative Representations of Belief

TL;DR

This paper explores how different quantitative belief measures align with qualitative belief structures, enhancing understanding and interpretation of belief representations in probability and belief function theories.

Contribution

It investigates the compatibility between various quantitative belief measures and qualitative belief structures, providing a foundation for better belief representation and interpretation.

Findings

Qualitative probability is compatible with monotonic belief functions.

Smets' generalized belief functions are compatible with a weaker belief structure.

Analysis supports the use of these measures for belief acquisition and interpretation.

Abstract

The compatibility of quantitative and qualitative representations of beliefs was studied extensively in probability theory. It is only recently that this important topic is considered in the context of belief functions. In this paper, the compatibility of various quantitative belief measures and qualitative belief structures is investigated. Four classes of belief measures considered are: the probability function, the monotonic belief function, Shafer's belief function, and Smets' generalized belief function. The analysis of their individual compatibility with different belief structures not only provides a sound b<msis for these quantitative measures, but also alleviates some of the difficulties in the acquisition and interpretation of numeric belief numbers. It is shown that the structure of qualitative probability is compatible with monotonic belief functions. Moreover, a belief structure slightly weaker than that of qualitative belief is compatible with Smets' generalized belief functions.