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On Some Subclasses of the Fodor-Roubens Fuzzy Bi-implication

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Logic, Language, Information and Computation (WoLLIC 2012)

Abstract

The paper deals with fuzzy versions of the classical bi-implication, that is, extensions of classical bi-implication to the canonical domain of mathematical fuzzy logics, the real-valued unit interval [0,1]. Our approach to fuzzy bi-implication may be summarized as follows: first, we recall a well-known approach to bi-implications, by Fodor and Roubens, via the direct axiomatization of the properties of the corresponding class of operators; next, we investigate a particular defining standard of bi-implication in terms of t-norms and r-implications. We study four prospective classes of bi-implications based on such defining standard, by varying the properties of its composing operators, and show that these classes collapse into precisely two increasingly weaker subclasses of the Fodor-Roubens bi-implication.

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Callejas, C., Marcos, J., Callejas Bedregal, B.R. (2012). On Some Subclasses of the Fodor-Roubens Fuzzy Bi-implication. In: Ong, L., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2012. Lecture Notes in Computer Science, vol 7456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32621-9_15

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  • DOI: https://doi.org/10.1007/978-3-642-32621-9_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32620-2

  • Online ISBN: 978-3-642-32621-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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