Abstract
The paper studies and proposes the requirements that a conditioning rule of Evidence theory should satisfy, and a new conditioning rule satisfying them. It also proposes a generalized conditioning rule that abandons one of the requirements. The proposed requirements are i) focal elements of a conditional basic belief assignment are limited to subsets of a set representing the condition, ii) conditional bba must be defined except the case where the condition set is empty and iii) bba conditioned by the universal set equals bba without any condition. The first requirement represents that the given condition is completely reliable, the second is derived from the interpretation that Evidence theory deals with beliefs in human minds, not uncertainty related to frequency, and the third is the result from the fact that the universal set contains all possible elements. The paper proposes a conditioning rule satisfying the above three requirements. Then, it generalizes the rule with abandoning the first requirement by introducing a degree of reliability. The generalized rule is equivalent to the one satisfying the three requirements when the degree is one, and to the original bba without any condition when the degree is zero. When the degree is between zero and one, the rule interpolates both the ends linearly. Numerical examples show the difference between the proposed rule and well-known conventional conditioning rules. They show that only the proposed one satisfies all the three requirements. In addition, they also show that instability that a little difference between two prior beliefs may produce a large difference between the posterior beliefs, which is observed in the case of conditioning with normalization such as Dempster' rule, is solved with the proposed conditioning rule.
