Representation and combination of uncertainty with belief functions and possibility measures

The theory of evidence proposed by G. Shafer is gaining more and more acceptance in the field of artificial intelligence, for the purpose of managing uncertainty in knowledge bases. One of the crucial problems is combining uncertain pieces of evidence stemming from several sources, whether rules or physical sensors. This paper examines the framework of belief functions in terms of expressive power for knowledge representation. It is recalled that probability theory and Zadeh's theory of possibility are mathematically encompassed by the theory of evidence, as far as the evaluation of belief is concerned. Empirical and axiomatic foundations of belief functions and possibility measures are investigated. Then the general problem of combining uncertain evidence is addressed, with focus on Dempster rule of combination. It is pointed out that this rule is not very well adapted to the pooling of conflicting information. Alternative rules are proposed to cope with this problem and deal with specific cases such as nonreliable sources, nonexhaustive sources, inconsistent sources, and dependent sources. It is also indicated that combination rules issued from fuzzy set and possibility theory look more flexible than Dempster rule because many variants exist, and their numerical stability seems to be better.