1. Dempster-Shafer Theory SIU CS 537 4/12/11 and 4/14/11 Chet Langin

2. Dempster, A. P. (1967). "Upper and Lower Probabilities Induced by a Multivalued Mapping.“ The Annals of Mathematical Statistics 38(2): 325-339. Shafer, G. (1976). A Mathematical Theory of Evidence, Princeton University Press.

3. What is Dempster-Shafer? Dempster-Shafer (D-S or DS) Mathematical theory of evidence. Data fusion. Degree of belief. Generalization of Bayes theory. Sets. Mass, not probability. “Bel Function” – Belief function

4. The D-S Environment

5. D-S Environment, Cont.

7. D-S vs. Probability

8. Non-belief vs. Ignorance

9. D-S Mass

10. Combining Evidence

11. D-S Rule of Combination

12. Example Combination Bomber = 0.63 + 0.27 = 0.90 Bomber or Fighter = 0.07 Non-belief = 0.03

13. Range of Belief

14. What Would Make Plausibility < 1?

15. Evidential Interval

16. Example Evidential Intervals [1, 1]Completely True [0, 0]Completely False [0, 1]Completely Ignorant [Bel, 1]Tends to support [0, Pls]Tends to refute [Bel, Pls]Tends to both support & refute

17. Bel vs. Bel()

18. Bel() Example

19. Combination of 2 Bel()

20. The Normalization of Belief

21. A New Table

22. Normalization

23. Normalization, Cont. OK!

24. New Evidential Interval Belief | Plausibility | Disbelief Belief | Plausibility