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Aggregation Functions in Theory and in Practise pp 429–440Cite as

Fuzzy Implication Classes Satisfying a Boolean-Like Law

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 228))

Abstract

Properties that are always true in the classical theory (Boolean laws) have been extended to fuzzy theory and so-called Boolean-like laws. The fact that they do not remain valid in any standard fuzzy set theory has induced a broad investigation. In this paper we show the sufficient and necessary conditions that a fundamental Boolean-like law—y ≤ I(x,y)—holds in fuzzy logics. We focus the investigation on the following classes of fuzzy implications: (S,N)-, R-, QL-, D-, (N,T)-, f-, g- and h-implications.

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Author information

Authors and Affiliations

  1. Federal Rural University of Semi-Árido - UFERSA, 59515-000, Angicos, RN, Brazil

    Anderson Cruz

  2. Federal University of Rio Grande do Norte - UFRN, 59072-970, Natal, RN, Brazil

    Benjamín Bedregal & Regivan Santiago

Authors
  1. Anderson Cruz
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  2. Benjamín Bedregal
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  3. Regivan Santiago
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Corresponding author

Correspondence to Anderson Cruz .

Editor information

Editors and Affiliations

  1. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Humberto Bustince

  2. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Javier Fernandez

  3. Department of Mathematics and, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  4. Department of Computer Science, Universidad de Alcalá de Henares, Madrid, Spain

    Tomasa Calvo

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Cruz, A., Bedregal, B., Santiago, R. (2013). Fuzzy Implication Classes Satisfying a Boolean-Like Law. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_41

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  • DOI: https://doi.org/10.1007/978-3-642-39165-1_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39164-4

  • Online ISBN: 978-3-642-39165-1

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