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Some Results on Extension of Lattice-Valued XOR, XOR-Implications and E-Implications

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 611))

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Abstract

The extension problem is an important and interesting issue that be addressed for many different classes of operator. For instance, one can thing who to extend a fuzzy operator from a lattice to a bigger one preserving its algebraic properties. In this paper we attempt to the extension of lattice-valued version of Xor (exclusive) operator using a special method based on retractions. Also we discuss about Xor-implications end E-implications.

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Notes

  1. 1.

    If f and g are functions on a lattice L it is said that \(f \leqslant g\) if and only if \(f(x) \leqslant _L g(x)\) for all \(x \in L\).

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Author information

Authors and Affiliations

  1. Programa de Pós-Graduação em Modelagem Computacional em Ciência e Tecnologia - PPGMC, Departamento de Ciências Exatas e Tecnológicas - DCET, Universidade Estadual de Santa Cruz - UESC, Ilhéus, BA, 45662-900, Brazil

    Eduardo Palmeira

  2. Departamento de Informtica e Matemtica Aplicada - DIMAp, Universidade Federal do Rio Grande do Norte - UFRN, Natal, RN, 59078-970, Brazil

    Benjamín Bedregal

Authors
  1. Eduardo Palmeira
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  2. Benjamín Bedregal
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Corresponding author

Correspondence to Eduardo Palmeira .

Editor information

Editors and Affiliations

  1. INESC-ID,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Joao Paulo Carvalho

  2. LIP 6, Université Pierre et Marie Curie, Paris, France

    Marie-Jeanne Lesot

  3. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  4. IDMEC,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Susana Vieira

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Iona College, Machine Intelligence Institute, New Rochelle, New York, USA

    Ronald R. Yager

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Palmeira, E., Bedregal, B. (2016). Some Results on Extension of Lattice-Valued XOR, XOR-Implications and E-Implications. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 611. Springer, Cham. https://doi.org/10.1007/978-3-319-40581-0_66

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  • DOI: https://doi.org/10.1007/978-3-319-40581-0_66

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40580-3

  • Online ISBN: 978-3-319-40581-0

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