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The Extension Principle of Zadeh and Fuzzy Numbers

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A First Course in Fuzzy Logic, Fuzzy Dynamical Systems, and Biomathematics

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

Abstract

This chapter presents the Extension Principle of Zadeh, and as the name suggests, it is a method used to extend to fuzzy set theory the typical operations of classical set theory. It gives the framework to calculate the membership degree of elements of a fuzzy set and functions of fuzzy sets, which are the result of operations. Also, in the context of fuzzy sets, the concepts of fuzzy number and fuzzy number arithmetic are introduced.

Everything has numbers and nothing can be understand without numbers.

(Philolaus, Pythagorean-C.470 - C.385 BCE)

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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). The Extension Principle of Zadeh and Fuzzy Numbers. 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_2

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  • DOI: https://doi.org/10.1007/978-3-662-53324-6_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53322-2

  • Online ISBN: 978-3-662-53324-6

  • eBook Packages: EngineeringEngineering (R0)

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