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Representations of Archimedean t-norms in interval-valued fuzzy set theory

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Abstract
In this paper the Archimedean property and the nilpotency of t-norms on the lattice L^I is investigated, where L^I is the underlying lattice of interval-valued fuzzy set theory (Sambuc, 1975) and intuitionistic fuzzy set theory (Atanassov, 1983). We give some characterizations of continuous t-norms on L^I which satisfy the residuation principle, T(D, D) ⊆ D, the Archimedean property and nilpotency.
Keywords
intuitionistic fuzzy set, interval-valued fuzzy set, t-norm, Archimedean, nilpotent, strict, representation

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Chicago
Deschrijver, Glad. 2007. “Representations of Archimedean T-norms in Interval-valued Fuzzy Set Theory.” In Proceedings of the 5th Conference of the European Society for Fuzzy Logic and Technology, ed. Martin Štěpnička, Vilém Novák, and Ulrich Bodenhofer, 53–60. University of Ostrava.
APA
Deschrijver, Glad. (2007). Representations of Archimedean t-norms in interval-valued fuzzy set theory. In M. Štěpnička, V. Novák, & U. Bodenhofer (Eds.), Proceedings of the 5th Conference of the European Society for Fuzzy Logic and Technology (pp. 53–60). Presented at the 5th International Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT2007), University of Ostrava.
Vancouver
1.
Deschrijver G. Representations of Archimedean t-norms in interval-valued fuzzy set theory. In: Štěpnička M, Novák V, Bodenhofer U, editors. Proceedings of the 5th Conference of the European Society for Fuzzy Logic and Technology. University of Ostrava; 2007. p. 53–60.
MLA
Deschrijver, Glad. “Representations of Archimedean T-norms in Interval-valued Fuzzy Set Theory.” Proceedings of the 5th Conference of the European Society for Fuzzy Logic and Technology. Ed. Martin Štěpnička, Vilém Novák, & Ulrich Bodenhofer. University of Ostrava, 2007. 53–60. Print.
@inproceedings{377800,
  abstract     = {In this paper the Archimedean property and the nilpotency of t-norms on the lattice L\^{ }I is investigated, where L\^{ }I is the underlying lattice of interval-valued fuzzy set theory (Sambuc, 1975) and intuitionistic fuzzy set theory (Atanassov, 1983). We give some characterizations of continuous t-norms on L\^{ }I which satisfy the residuation principle, T(D, D) \ensuremath{\subseteq} D, the Archimedean property and nilpotency.},
  author       = {Deschrijver, Glad},
  booktitle    = {Proceedings of the 5th Conference of the European Society for Fuzzy Logic and Technology},
  editor       = {\v{S}t\v{e}pni\v{c}ka, Martin and Nov{\'a}k, Vil{\'e}m and Bodenhofer, Ulrich},
  isbn         = {978-80-7368-386-3},
  language     = {eng},
  location     = {Ostrava, Czech Republic},
  pages        = {53--60},
  publisher    = {University of Ostrava},
  title        = {Representations of Archimedean t-norms in interval-valued fuzzy set theory},
  year         = {2007},
}