Compatibility of Quantitative and Qualitative Representations of Belief
This work addresses foundational issues in belief representation for AI and decision-making, providing a theoretical basis for quantitative measures and easing difficulties in acquiring and interpreting numeric beliefs, though it is incremental in nature.
The paper investigates the compatibility between quantitative belief measures (probability, monotonic belief, Shafer's belief, and Smets' generalized belief functions) and qualitative belief structures, showing that qualitative probability is compatible with monotonic belief functions and a weaker belief structure is compatible with Smets' generalized belief functions.
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.