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Restricted Equivalence Function on L([0, 1])

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Fuzzy Logic in Intelligent System Design (NAFIPS 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 648))

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Abstract

It is know from the literature that interval-valued equivalence functions are not decomposable. In order to solve that problem and give a characterization for interval-valued restricted equivalence functions by means of aggregating interval fuzzy implication we consider an admissible order on the lattice L([0, 1]). Also, we discuss about some other properties of those operators.

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Notes

  1. 1.

    A non-empty set P endowed with a partial order \(\leqslant _P\) is called a partial order set or for short a poset.

  2. 2.

    An element e is called an equilibrium point if \(N(e) = e\).

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Author information

Authors and Affiliations

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

    Eduardo S. Palmeira

  2. Depto. de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, Natal, 59078-970, Brazil

    Benjamín Bedregal

Authors
  1. Eduardo S. Palmeira
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  2. Benjamín Bedregal
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Corresponding author

Correspondence to Eduardo S. Palmeira .

Editor information

Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Patricia Melin

  2. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  4. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada

    Marek Reformat

  5. Laboratory of Computational Intelligence and Automation, University of Waterloo, Waterloo, Ontario, Canada

    William Melek

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Palmeira, E.S., Bedregal, B. (2018). Restricted Equivalence Function on L([0, 1]). In: Melin, P., Castillo, O., Kacprzyk, J., Reformat, M., Melek, W. (eds) Fuzzy Logic in Intelligent System Design. NAFIPS 2017. Advances in Intelligent Systems and Computing, vol 648. Springer, Cham. https://doi.org/10.1007/978-3-319-67137-6_45

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  • DOI: https://doi.org/10.1007/978-3-319-67137-6_45

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67136-9

  • Online ISBN: 978-3-319-67137-6

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