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On copulas, quasicopulas and fuzzy logic

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Abstract

We investigate (quasi)copulas as possible truth functions of fuzzy conjunction which is not necessarily associative and present some axiom systems for such fuzzy logics. In particular, we study an expansion of Łukasiewicz (infinite valued propositional) logic by a new connective interpreted as an arbitrary quasicopula (and also by a new connective interpreted as the residuum of the copula). Main results concern standard completeness.

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Authors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 2, 182 07, Prague, Czech Republic

    Petr Hájek

  2. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of technology, 81368, Bratislava, Slovakia

    Radko Mesiar

  3. IRAFM University of Ostrava, 70103, Ostrava, Czech Republic

    Radko Mesiar

Authors
  1. Petr Hájek
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  2. Radko Mesiar
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Correspondence to Petr Hájek.

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Hájek, P., Mesiar, R. On copulas, quasicopulas and fuzzy logic. Soft Comput 12, 1239–1243 (2008). https://doi.org/10.1007/s00500-008-0286-z

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  • DOI: https://doi.org/10.1007/s00500-008-0286-z

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