IPMU 1990: Uncertainty in Knowledge Bases pp 58-67

# Updating uncertain information

• Serafín Moral
• Luis M. De Campos
1. Mathematical Theory Of Evidence
Part of the Lecture Notes in Computer Science book series (LNCS, volume 521)

## Abstract

In this paper, it is considered the concept of conditioning for a family of possible probability distributions. First, the most used definitions are reviewed, in particular, Dempster conditioning, and upper-lower probabilities conditioning. It is shown that the former has a tendency to be too informative, and the last, by the contrary, too uninformative. Another definitions are also considered, as weak and strong conditioning. After, a new concept of conditional information is introduced. It is based on lower-upper probabilities definition, but introduces an estimation of the true probability distribution, by a method analogous to statistical maximum likelihood.

Finally, it is deduced a Bayes formula in which there is no ’a prior’ information. This formula is used to combine informations from different sources and its behavior is compared with Dempster formula of combining informations. It is shown that our approach is compatible with operations with fuzzy sets.

## Keywords

Theory of Evidence conditioning combining informations Bayes rule

## References

1. [1]
Campos L.M. de,Lamata M.T.,Moral S.(1989) The concept of conditional fuzzy measure. International Journal of Intelligent Systems 5, 237–246.Google Scholar
2. [2]
Dempster A.P. (1967) Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Statist. 38, 325–339.Google Scholar
3. [3]
Dubois D., Prade H. (1986) On the unicity of Dempster rule of combination. International Journal of Intelligent Systems 1, 133–142.Google Scholar
4. [4]
Fagin R., Halpern J.Y. (1989) Updating beliefs vs. combining beliefs. Unpublished Report.Google Scholar
5. [5]
Lamata M.T., Moral S.(1989) Classification of fuzzy measures. Fuzzy Sets and Systems 33, 243–253.
6. [6]
Pearl J. (1988) Probabilistic Reasoning in Intelligent Systems. Morgan & Kaufman (San Mateo).Google Scholar
7. [7]
Pearl J. (1989) Reasoning with belief functions: a critical assessment. Tech. Rep. R-136. University of California, Los Angeles.Google Scholar
8. [8]
Planchet B. (1989) Credibility and Conditioning. Journal of Theoretical Probability 2, 289–299.
9. [9]
Shafer G. (1976) A Theory of Statistical Evidence. In: Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. II (Harper, Hooker, eds.) 365–436.Google Scholar
10. [10]
Smets Ph. (1978) Un modele mathematico-statistique simulant le procesus du diagnostic medical. Doctoral Dissertation, Universite Libre de Bruxelles. Bruxelles.Google Scholar
11. [11]
Smets Ph., Kennes (1989) The transferable belief model: comparison with bayesian models. Technical Report, IRIDIA-89.Google Scholar