Probabilities: A Historical Perspective - Information Fusion in Signal and Image Processing - page 271

Appendix B
Axiomatic Inference of the Dempster-Shafer
Combination Rule
The Dempster-Shafer belief theory has often been criticized for imposing an ad
hoc combination rule (Dempster's orthogonal rule [SHA 76], equation [7.26]), with
no theoretical justification for it, although it does have a perfectly satisfactory intuitive
interpretation, which is in agreement with the concept of the conjunction of focal
elements.
This appendix completes the theory presented in Chapter 7 by giving a theoretical
justification of the conjunctive combination rule (non-normalized, as it is suggested in
[SME 90]).
We will also explain how it is related to the Cox approach to probabilities, which is
presented in Appendix A. In particular, we will underline the differences between the
axioms, which explain the difference between the models and the combination modes
in the two theories.
Several recent works have attempted to justify this rule, for example, those of
Dubois and Prade [DUB 86], which mathematically justify the use of the product to
combine masses based on the concept of the separability of sources, or those of Smets
based on the transferable belief model [SME 90].