Belief Combination by Means of Frame Transformations (extended Abstract)

Approximate reasoning in the presence of multiple sources of information requires a mechanism to combine diierent measures representing uncertainty, belief, or desirability into a single aggregate measure that reeects contributions of the individual information sources. This may be achieved by constructing an appropriate combination operator. Speciic combination operators are provided by formalisms such as probability theory and Dempster-Shafer evidence theory. Various ad-hoc approaches to combination have also been proposed, a classical example being the MYCIN calculus of certainty factors. We have developed a theory that describes combination operators in terms of frames of reference on the space in which the measures to be combined take their values; diierent combination operators correspond to the same canonical form as viewed in diierent frames of reference. Our theory provides an algorithm that is guaranteed to extract a suitable reference frame directly from the combination operator whenever such a frame exists. This allows us to show that previously considered combination operators , including MYCIN-like and probabilistic operators, are encompassed by our theory. New families of combination operators are also made available. Furthermore, our theoretical framework provides a natural nonlinear scaling mechanism that facilitates experimental tuning of the resulting operators.