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Enric Trillas: A Passion for Fuzzy Sets pp 93–108Cite as

Generation of Interval-Valued Fuzzy Negations from Trillas’ Theorem. The Case of Interval Type-2 Fuzzy Sets

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ,volume 322)

Abstract

In this work we introduce a method for building interval-valued negations using the characterization theorem for strong negations which was proposed by Trillas in 1979. We also show that interval type-2 fuzzy sets are a three dimensional representation of interval-valued fuzzy sets and we analyze the problems to build complementation for such interval type-2 fuzzy sets. We finally propose a method to construct this complementation.

Keywords

  • Interval-valued negation
  • Interval-valued fuzzy sets
  • Interval type 2 fuzzy set
  • Complementation.

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Acknowledgments

This paper has been partially supported by the National Science Foundation of Spain, Grants TIN2013-40765-P and TIN2012-32482.

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Authors and Affiliations

  1. Departamento de Automática Y Computación, Universidad Pública de Navarra, Campus Arrosadia s/n, 31006, Pamplona, Spain

    H. Bustince, E. Barrenechea, J. Fernández & M. Pagola

  2. Faculty of Mathematics, Complutense University, 28040, Madrid, Spain

    J. Montero

Authors
  1. H. Bustince
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  2. E. Barrenechea
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  3. J. Fernández
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  4. M. Pagola
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  5. J. Montero
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Corresponding author

Correspondence to H. Bustince .

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Editors and Affiliations

  1. European Centre for Soft Computing, Asturias, Spain

    Luis Magdalena

  2. Depto. de Ciencias de la Computación e Inteligencia Artificial, University of Granada, Granada, Spain

    Jose Luis Verdegay

  3. Spanish Council for Scientific Research (CSIC), Artificial Intelligence Research Institute (IIIA-CSIC), Catalonia, Spain

    Francesc Esteva

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Bustince, H., Barrenechea, E., Fernández, J., Pagola, M., Montero, J. (2015). Generation of Interval-Valued Fuzzy Negations from Trillas’ Theorem. The Case of Interval Type-2 Fuzzy Sets. In: Magdalena, L., Verdegay, J., Esteva, F. (eds) Enric Trillas: A Passion for Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 322. Springer, Cham. https://doi.org/10.1007/978-3-319-16235-5_8

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  • DOI: https://doi.org/10.1007/978-3-319-16235-5_8

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