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Structure Of Girard Monoids On [0,1]

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Topological and Algebraic Structures in Fuzzy Sets

Part of the book series: Trends in Logic ((TREN,volume 20))

Abstract

The structure of commutative, residuated, zero closed, lattice-ordered, integral monoids—in other words, Girard monoids—is investigated, when the underlying universe is the unit interval [0, 1]. On [0,1], the notion of a Girard monoid coincides with the notion of a left-continuous triangular norm with strong induced negation. Thus, this chapter investigates the structure of left-continuous triangular norms with strong induced negations. Based on an exhaustive geometrical description we discuss how to construct and how to decompose such triangular norms. Further, theorems are established on their continuity and integrality.

Supported by the National Scientific Research Fund Hungary (OTKA F/032782) and by the Higher Education Research and Development Programme Hungary (FKFP 0051/2000).

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Authors
  1. S. Jenei
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Youngstown State University, 44555-3609, Youngstown, Ohio, USA

    Stephen Ernest Rodabaugh

  2. Institut für Algebra, Stochastik und wissensbasierte mathematische Systeme, Johannes Kepler Universität, 4040, Linz, Austria

    Erich Peter Klement

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Jenei, S. (2003). Structure Of Girard Monoids On [0,1]. In: Rodabaugh, S.E., Klement, E.P. (eds) Topological and Algebraic Structures in Fuzzy Sets. Trends in Logic, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0231-7_12

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  • DOI: https://doi.org/10.1007/978-94-017-0231-7_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6378-6

  • Online ISBN: 978-94-017-0231-7

  • eBook Packages: Springer Book Archive

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