# Combining Evidence in the Extended Dempster-Shafer Theory

• Jiwen Guan
• Jasmina Pavlin
• Victor R. Lesser
Conference paper
Part of the Workshops in Computing book series (WORKSHOPS COMP.)

## Abstract

The Dempster-Shafer (D-S) theory of evidence generalizes Bayesian probability theory, by providing a coherent representation for ignorance (lack of evidence). However, uncertain relationships between evidence and hypotheses bearing on this evidence are difficult to represent in applications of the theory. Yen [1] extended the theory by introducing a probabilistic mapping that uses conditional probabilities to express these uncertain relationships, and developed a three-step method for combining evidence from different evidential sources. We present a simpler, one-step method for combining evidence based on the extended D-S theory, and prove that it gives the same results.

## Keywords

Belief Function Hypothesis Space Focal Element Basic Probability Assignment Evidential Source
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. [1]
Yen, J., “A reasoning model based on an extended Dempster-Shafer theory”, Proceedings aaai-86 125–131.Google Scholar
2. [2]
Dempster, A. P., “Upper and lower probabilities induced by a multi-valued mapping”, Annals of mathematical statistics, 38 (1967) 325–339.
3. [3]
Dempster, A. P., “A generalization of Bayesian inference”, J. Roy. Statist. Soc. B, 30 (1968) 205–247.
4. [4]
Duda, R. O., P. E. Hart, and N. J. Nilsson,“Subjective Bayesian methods for rule-based inference systems”, Proceedings 1976 National Computer Conference, AFIPS, 45 (1976) 1075–1082.Google Scholar
5. [5]
Gordon, J. and E. H. Shortliffe, “A method for managing evidential reasoning in a hierarchical hypothesis space”, Artificial Intelligence, 26 (1985) 323–357.
6. [6]
Grosof, B. N.,“Evidential confirmation as transformed probability”, Proceedings of the AAAI/IEEE Workshop on Uncertainty and Probability in Artificial Intelligence, 1985, pp. 185–192.Google Scholar
7. [7]
Heckerman, D., “A probabilistic interpretation for MYCIN’s certainty factors”, Proceedings of the AAAI/IEEE Workshop on Uncertainty and Probability in Artificial Intelligence, 1985, pp. 9–20.Google Scholar
8. [8]
Loui, R., J. Feldman, H. Kyburg,“Interval-based decisions for reasoning systems”, Proceedings of the AAAI/IEEE Workshop on Uncertainty and Probability in Artificial Intelligence, 1985, pp. 193–200.Google Scholar
9. [9]
Hudlicka E., Lesser V. R., Pavlin J. Rewari A, “Design of a Distributed Fault Diagnosis System”, Technical Report 86–63, COINS Department, University of Massachusetts, Amherst, Massachusetts.Google Scholar
10. [10]
Shafer, G., “A Mathematical Theory of Evidence”, Princeton University Press, Princeton, New Jersey, 1976.Google Scholar
11. [11]
Yen, J., “GERTIS: A Dempster-Shafer approach to diagnosing hierarchical hypotheses”, Communications of the ACM, 1989 573–585.Google Scholar

## Authors and Affiliations

• Jiwen Guan
• 1
• Jasmina Pavlin
• 2
• Victor R. Lesser
• 2
1. 1.Department of Information SystemsUniversity of Ulster at JordanstownNewtownabbeyUK
2. 2.Department of Computer and Information ScienceUniversity of MassachusettsAmherstUSA