Abstract
The aim of the paper is to show that the combination of conditional evidence, which is the cornerstone of Zadeh’s theory of approximate reasoning and of the theory of expert systems, can be sometimes done within certain probabilistic framework. This type of reasoning can be also characterized as a suggestion to cope with the situation described by a large number of data by constructing a rough simplifying probabilistic model. Further as a byproduct, some properties of the conditional probability of fuzzy sets on the Cartesian product are obtained.
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References
P.Smets, Probability of a fuzzy event:an axiomatic approach, Fuzzy sets and systems 7(1982) 165–189.
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L.A.Zadeh, The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets and Systems 11 (1983) 199–227.
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© 1988 Springer-Verlag Berlin Heidelberg
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Sustal, J. (1988). On the Combination of Vague Evidence of the Probabilistic Origin. In: Kacprzyk, J., Fedrizzi, M. (eds) Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making. Lecture Notes in Economics and Mathematical Systems, vol 310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46644-1_10
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DOI: https://doi.org/10.1007/978-3-642-46644-1_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50005-6
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