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A First Course in Fuzzy Logic, Fuzzy Dynamical Systems, and Biomathematics pp 135–173Cite as

Measure, Integrals and Fuzzy Events

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

Abstract

This chapter reviews classical measure theory including probability and Lebesgue measures. This discussion is followed by fuzzy measures, Sugeno measures, and possibilistic measures in order to understand the integration of Lebesgue, Choquet and Sugeno. These concepts are used in the development of fuzzy expected value. Lastly, the chapter closes with a discussion of the concepts of fuzzy event, the probability of a fuzzy event, dependence of fuzzy events, independence of fuzzy events, together with the concepts of random linguistic variables and random fuzzy variables.

In every field of knowledge, there is a tendency for the quantitative, for the measure. So, it can be stated that the scientific study of each branch of knowledge begins when a measure is introduced and the study of quantitative variation is the evolution of the qualitative.

(B. J. Caraça)

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Notes

  1. 1.

    Adapted from Murofushi [4].

  2. 2.

    Adapted from Bezdek [12 ] .

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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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Correspondence to Laécio Carvalho de Barros .

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de Barros, L.C., Bassanezi, R.C., Lodwick, W.A. (2017). Measure, Integrals and Fuzzy Events. 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_7

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  • DOI: https://doi.org/10.1007/978-3-662-53324-6_7

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