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Distribution functions

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Triangular Norms

Part of the book series: Trends in Logic ((TREN,volume 8))

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Abstract

One basic idea in probability theory is to replace numbers by distribution functions, taking into account the fact that in many measurements a smaller or larger amount of uncertainty cannot be avoided. In [Schweizer & Sklar 1983, page 123] distribution functions were even expected to be “numbers of the future”. Obviously, the revolutionary developments in physics and chemistry (in particular relativity and quantum theory, and statistical mechanics) in the first decades of the twentieth century provided a strong motivation for such considerations.

... leads to the concept of a space in which a distribution function rather than a definite number is associated with every pair of elements. [...] The distribution function associated with two elements of a statistical metric space might be said to give, for every z, the probability that the distance between the two points in question does not exceed z. Such a statistical generalization of metric spaces appears to be well adapted for the investigation of physical quantities and physiological thresholds. The idealization of the local behavior of rods and boards, implied by this statistical approach, differs radically from that of Euclid. In spite of this fact, or perhaps just because of it, the statistical approach may provide a useful means for geometrizing the physics of the microcosm.

Karl Menger

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© 2000 Springer Science+Business Media Dordrecht

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Klement, E.P., Mesiar, R., Pap, E. (2000). Distribution functions. In: Triangular Norms. Trends in Logic, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9540-7_9

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  • DOI: https://doi.org/10.1007/978-94-015-9540-7_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5507-1

  • Online ISBN: 978-94-015-9540-7

  • eBook Packages: Springer Book Archive

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