Actions of Automorphisms on Some Classes of Fuzzy Bi-implications

• Autores: C Callejas, Jorge Marcos Acevedo , Benjamín Bedregal
• Localización: Mathware & soft computing: The Magazine of the European Society for Fuzzy Logic and Technology, ISSN-e 1134-5632, Vol. 20, Nº. 1, 2013, págs. 94-97
• Idioma: inglés
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• Resumen

  • In a previous paper we have studied two classes of fuzzy bi-implications based on t-norms and r-implications, and shown that they constitute increasingly weaker subclasses of the Fodor-Roubens bi-implication. Now we prove that each of these three classes of bi-implications is closed under automorphisms.

• Referencias bibliográficas
  • M. Baczy«ski. Residual implications revisited. Notes on the Smets-Magrez Theorem. Fuzzy Sets and Systems, 145(2): 267-277, 2004.
  • M. Baczyski and B. Jayaram. Fuzzy Implications. Studies in Fuzziness and Soft Computing. Springer, 2008.
  • H. Bustince, P. Burillo, and F. Soria. Automorphisms, negations and implication operators. Fuzzy Sets and Systems, 134:209-229, 2003.
  • H. Bustince, E. Barrenechea, and M. Pagola. Restricted equivalence functions. Fuzzy Sets and Systems, 157(17): 2333-2346, 2006.
  • C. Callejas, J. Marcos and B. R. C. Bedregal. On some subclasses of the Fodor-Roubens fuzzy biimplication, in Proceedings of the XIX Workshop...
  • J. Fodor and M. Roubens. Fuzzy Preference Modelling and Multicriteria Decision Support. Theory and Decision Library. Kluwer, 1994.
  • T.W. Hungerford. Algebra. Graduate texts in mathematics, Springer-Verlag, 2000.
  • E.P. Klement, R. Mesiar, and E. Pap. Triangular Norms. Trends in Logic: Studia Logica Library. Kluwer, 2000.
  • E. Trillas. Sobre funciones de negación en la teoria de conjuntos difusos. Stochastica, 3:47-59, 1979.