Abstract
In about thirty pages, it is not easy to condense a such subject, but we did our best. The reader will find a study of four main associations between fuzzy subsets and probabilities. The first part will concern hybrid numbers where the reader will find a way to add fuzzy numbers and random variables without deterioration of the level of information available. The second part is devoted to random fuzzy subsets which are specially important when the valuation is not the decision of one expert but several. It is also a generalization of both : fuzzy subset theory and probability theory. The third part recalls that probabilization of fuzzy subsets obeys to the same rules than ordinary subsets. Lastly, we show the theory of belief functions which are an interesting construction for some problems of diagnosis and decision ; several extensions are also offered.
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Short Bibliography
Hybrid numbers
A. Kaufmann and M.M. Gupta.-Introduction to fuzzy arithmetic. Publ. Van Nostrand. Reinhold.-1985.
A. Kaufmann.-Distance et relation d’ordre pour les nombres hybrides.-Note de travail N° 122.-A. Kaufmann.-Consultant.-Corenc-Montfleury.-France.-1984.
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Random fuzzy subsets
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Probability of fuzzy events
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Belief functions
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© 1986 D. Reidel Publishing Company
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Kaufmann, A. (1986). Hybrid Data – Various Associations Between Fuzzy Subsets and Random Variables. In: Jones, A., Kaufmann, A., Zimmermann, HJ. (eds) Fuzzy Sets Theory and Applications. NATO ASI Series, vol 177. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4682-8_10
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DOI: https://doi.org/10.1007/978-94-009-4682-8_10
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