Abstract
Probability is one of the most common examples of valuation function. The relationship between subsets is expressed by their joint probability and gives rise to the concept of statistical dependence. In fuzzy logic this relationship is based in connection properties. The aim of this work is to analyse how valuations about subsets may be made. In a first part some theorems are recalled in order to situate the essential role of connectives as t-norms, then the equivalence between Fuzzy Logic’s and probabilistic spaces is proven when Frank’s t-norms are used. Dependence and independence between subsets are analysed under the light of the previous results, and gives rise to a new concept of dependence degree, as well as its possible use in uncertain reasoning schemes.
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© 2002 Springer-Verlag Berlin Heidelberg
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Aguilar-Martin, J. (2002). Independence and Conditioning in a Connectivistic Fuzzy Logic Framework. In: Grzegorzewski, P., Hryniewicz, O., Gil, M.Á. (eds) Soft Methods in Probability, Statistics and Data Analysis. Advances in Intelligent and Soft Computing, vol 16. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1773-7_3
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DOI: https://doi.org/10.1007/978-3-7908-1773-7_3
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1526-9
Online ISBN: 978-3-7908-1773-7
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