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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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
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