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A First Course in Fuzzy Logic, Fuzzy Dynamical Systems, and Biomathematics pp 1–21Cite as

Fuzzy Sets Theory and Uncertainty in Mathematical Modeling

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 347))

Abstract

This chapter presents a brief discussion about uncertainty based on philosophical principles, mainly from the point of view of the pre-Socratic philosophers. Next, the notions of fuzzy sets and operations on fuzzy sets are presented. Lastly, the concepts of alpha-level and the statement of the well-known Negoita-Ralescu Representation Theorem, the representation of a fuzzy set by its alpha-levels, are discussed.

Man is the measure of all things: of things which are, that they are, and of things which are not, that they are not.

(Protagoras – 5th Century BCE)

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References

  1. L.A. Zadeh, Fuzzy sets. Inf. Control 8, 338–353 (1965)

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  2. B.J. Caraça, Conceitos fundamentais da matemática, 4th edn. (Gradiva Publicações Ltda, Lisboa, 2002)

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  3. C.V. Negoita, D.A. Ralescu, Applications of Fuzzy Sets to Systems Analysis (Wiley, New York, 1975)

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Author information

Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidade Estadual de Campinas, São Paulo, Brazil

    Laécio Carvalho de Barros

  2. Centro de Matemática e Computação, Universidade Federal do ABC, Santo André, São Paulo, Brazil

    Rodney Carlos Bassanezi

  3. Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, Colorado, USA

    Weldon Alexander Lodwick

Authors
  1. Laécio Carvalho de Barros
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  2. Rodney Carlos Bassanezi
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  3. Weldon Alexander Lodwick
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Corresponding author

Correspondence to Laécio Carvalho de Barros .

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de Barros, L.C., Bassanezi, R.C., Lodwick, W.A. (2017). Fuzzy Sets Theory and Uncertainty in Mathematical Modeling. In: A First Course in Fuzzy Logic, Fuzzy Dynamical Systems, and Biomathematics. Studies in Fuzziness and Soft Computing, vol 347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53324-6_1

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  • DOI: https://doi.org/10.1007/978-3-662-53324-6_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53322-2

  • Online ISBN: 978-3-662-53324-6

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