Axiomatization of qualitative belief structure

There are important theoretical and practical reasons to study belief structures. Similar to qualitative probability, qualitative belief can also be described in terms of a preference relation. One of the objectives in this study is to specify the precise conditions that a preference relation must satisfy such that it can be faithfully represented by a belief function. Two special classes of preference relations identified are weak and strict belief relations. It is shown that only strict belief relations are consistent (compatible) with belief functions. More importantly, the axiomatization of qualitative belief provides a foundation to develop a utility theory for decision making based on belief functions. The established relationship between qualitative probability and qualitative belief may also lead to a better understanding and useful applications of belief structures in approximate reasoning.