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Granular, Soft and Fuzzy Approaches for Intelligent Systems pp 3–25Cite as

On the Meaning and the Measuring of ‘Probable’

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 344))

Abstract

Probability has, as a mathematical theory that is an important part of pure mathematics, a long and distinguished history of more than 300 years, with fertile applications in almost all domains of science and technology; but the history of fuzzy sets only lasts 50 years, during which it was theoretically developed and successfully applied in many fields. From the very beginning there was, and there still is, a controversy on the nature of fuzzy sets viewed by its researchers far from randomness, and instead close by probabilists. This paper only goal is nothing else than trying to contribute to the clarification on the differences its authors see between fuzzy sets and probabilities and through the representation, or scientific domestication, of meaning by quantities.

To Professor Ron.R. Yager, with deep affection.

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Notes

  1. 1.

    For a detailed history of the theory of Fuzzy sets and its applications see the second author’s book [17].

  2. 2.

    The authors referred to the book Fuzzy Set Theory—and its Applications of the fuzzy-pioneer Zimmermann [35].

  3. 3.

    BISC Group is the mailing list of the Berkeley Initiative in Soft Computing (Majordomo@EECS.Berkeley.EDU).

  4. 4.

    Bayesianism or Bayesian probability theory is named after the English mathematician and Presbyterian Thomas Bayes (1701–1761) but it was popularized by Laplace.

  5. 5.

    For the cited papers see: [16, 27, 33].

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Acknowledgments

First author work is partially supported by the Foundation for the Advancement of Soft Computing (Asturias, Spain).

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Authors and Affiliations

  1. European Centre for Soft Computing, Mieres (Asturias), Spain

    Enric Trillas

  2. Institute of History of Medicine, Natural Sciences and Technology “Ernst-Haeckel-Haus”, Friedrich Schiller University Jena, Jena, Germany

    Rudolf Seising

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  1. Enric Trillas
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  2. Rudolf Seising
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Correspondence to Rudolf Seising .

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Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  2. Research and Innovation Center, Ford Motor Company, Dearborn, Michigan, USA

    Dimitar Filev

  3. Deakin University, Burwood, Victoria, Australia

    Gleb Beliakov

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Trillas, E., Seising, R. (2017). On the Meaning and the Measuring of ‘Probable’. In: Kacprzyk, J., Filev, D., Beliakov, G. (eds) Granular, Soft and Fuzzy Approaches for Intelligent Systems. Studies in Fuzziness and Soft Computing, vol 344. Springer, Cham. https://doi.org/10.1007/978-3-319-40314-4_1

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  • DOI: https://doi.org/10.1007/978-3-319-40314-4_1

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