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(T, N)-Implications and Some Functional Equations

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Fuzzy Information Processing (NAFIPS 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 831))

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Abstract

Fuzzy implications has drawn attention of many authors along the years, as their theoretical features seem to be a useful tool in a fair amount of applications. Meanwhile, functional equations are those in which the unknowns are functions instead of a traditional variable, and within the fuzzy logic, they can be considered generalizations of some tautologies of the classical logic. In this paper we investigate the validity of five functional equations for the class of (T, N)-implications, namely, we have selected the law of importation and four distributivity properties and have studied them in the context of the aforementioned operator.

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Acknowledgments

This work was partially supported by the Brazilian funding agency CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), under the processes No. 306970/2013-9 and 307781/2016-0.

Author information

Authors and Affiliations

  1. Group for Theory of Computation, Logic and Fuzzy Mathematics, Center of Exact and Natural Sciences, Rural Federal University of SemiArid (UFERSA), Mossoró, RN, Brazil

    Jocivania Pinheiro

  2. Group for Logic, Language, Information, Theory and Applications (LoLITA), Informatics and Applied Mathematics Department, Federal University of Rio Grande do Norte (UFRN), Natal, RN, Brazil

    Jocivania Pinheiro, Benjamin Bedregal & Regivan Santiago

  3. Centro de Ciências Computacionais, Federal University of Rio Grande (FURG), Rio Grande, RS, Brazil

    Helida Santos & Graçaliz Pereira Dimuro

Authors
  1. Jocivania Pinheiro
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  2. Benjamin Bedregal
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  3. Regivan Santiago
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  4. Helida Santos
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  5. Graçaliz Pereira Dimuro
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Corresponding author

Correspondence to Jocivania Pinheiro .

Editor information

Editors and Affiliations

  1. Department of Teleinformatics Engineering, Federal University of Ceará, Fortaleza, Ceará, Brazil

    Guilherme A. Barreto

  2. Department of Statistics & Applied Mathematics, Federal University of Ceará, Fortaleza, Ceará, Brazil

    Ricardo Coelho

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Pinheiro, J., Bedregal, B., Santiago, R., Santos, H., Dimuro, G.P. (2018). (T, N)-Implications and Some Functional Equations. In: Barreto, G., Coelho, R. (eds) Fuzzy Information Processing. NAFIPS 2018. Communications in Computer and Information Science, vol 831. Springer, Cham. https://doi.org/10.1007/978-3-319-95312-0_26

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  • DOI: https://doi.org/10.1007/978-3-319-95312-0_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-95311-3

  • Online ISBN: 978-3-319-95312-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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