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.
For a detailed history of the theory of Fuzzy sets and its applications see the second author’s book [17].
- 2.
The authors referred to the book Fuzzy Set Theory—and its Applications of the fuzzy-pioneer Zimmermann [35].
- 3.
BISC Group is the mailing list of the Berkeley Initiative in Soft Computing (Majordomo@EECS.Berkeley.EDU).
- 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.
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First author work is partially supported by the Foundation for the Advancement of Soft Computing (Asturias, Spain).
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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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