Hybrid Data – Various Associations Between Fuzzy Subsets and Random Variables

  • A. Kaufmann
Part of the NATO ASI Series book series (ASIC, volume 177)


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.


Fuzzy Number Distributive Lattice Mathematical Expectation Fuzzy Subset Belief Function 
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Short Bibliography

Hybrid numbers

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Belief functions

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Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • A. Kaufmann
    • 1
  1. 1.Ingénieur MathématicienUSA

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