Approximate Reasoning for Processing Uncertainty
Hamid Seridi* and Herman Akdag*,**
*LERI, Universite de Reims Rue des Crayères, BP 1035 51687 Reims cedex 2, France
**LIP6, Université P. & M. Curie 4, Place Jussieu Boîte 169 75687 Paris Cedex 05 France
In Bayesian networks as well as in knowledge-based systems, uncertainty in propositions can be represented by various degrees of belief encoded by qualitative values. In this paper, we present a qualitative approach of classical probability theory in the particular case where the set of probability degrees is replaced by a totally ordered set of symbolic values. We first define the four elementary operations (addition, subtraction, multiplication and division) allowing to manipulate these symbolic degrees of uncertainty, then we propose an axiomatic. The properties obtained from this axiomatic allows to show that our theory constitutes a qualitative approach for processing uncertain statements of natural language. The obtained results are usable in inferential processes as well as in Bayesian networks.
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