Abstract
There exist several ways for conditioning belief functions (Bel) in the Dempster-Shafer theory of evidence. One of them is the conventional Dempster's rule of conditioning. In the conditioning, Bel is updated based on information claiming that a certain proposition, say B, is true. Evidence is not always complete enough to prove that the single proposition, B, is true. Dubois and Prade have proposed a belief updating mechanism in which several propositions (say, Bi's) can be possibly true. The belief updating is done by applying the Dempster's rule of conditioning to each proposition Bi.
This paper clarifies problems which are caused by the use of the Dempster's rule of conditioning in the Dubois and Prade's mechanism. The problems are: (1) the Dempster's conditioning imposes strict (maybe too strict) requirement on a prior Bel, and (2) an updated Bel can be completely irrelevant to a prior Bel in some situation. We propose in this paper a new rule of conditioning to resolve the above problems. Compared with the conventional Dempster's rule of conditioning, our conditioning rule is less restrictive in the sense that a broader class of Bel's can be conditionalized. Our rule of conditioning thus enables the Dubois and Prade's belief updating mechanism useful in more general settings. Another distinctive feature of our conditioning rule is that a prior Bel can be conditionalized flexibly through an appropriate choice of a value for the continuous parameter in the conditioning rule.
