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Abstract
In this paper we study generators of t-norms on the lattice L^I of closed subintervals of the unit interval. Starting from a minimal set of axioms that any addition and multiplication operator on L^I must fulfill, we investigate the properties of the additive and multiplicative generators on L^I obtained using these arithmetic operators. We also investigate under which conditions the generators on L^I generate a t-norm.
Keywords
triangular norm, interval-valued fuzzy set, additive generator

Citation

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Chicago
Deschrijver, Glad. 2008. “Additive Generators in Interval-valued Fuzzy Set Theory.” In Proceedings of the 12th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, ed. Luis Magdalena, Manuel Ojeda-Aciego, and José Luis Verdegay, 1336–1343.
APA
Deschrijver, Glad. (2008). Additive generators in interval-valued fuzzy set theory. In L. Magdalena, M. Ojeda-Aciego, & J. L. Verdegay (Eds.), Proceedings of the 12th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (pp. 1336–1343). Presented at the 12th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2008).
Vancouver
1.
Deschrijver G. Additive generators in interval-valued fuzzy set theory. In: Magdalena L, Ojeda-Aciego M, Verdegay JL, editors. Proceedings of the 12th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. 2008. p. 1336–43.
MLA
Deschrijver, Glad. “Additive Generators in Interval-valued Fuzzy Set Theory.” Proceedings of the 12th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Ed. Luis Magdalena, Manuel Ojeda-Aciego, & José Luis Verdegay. 2008. 1336–1343. Print.
@inproceedings{623959,
  abstract     = {In this paper we study generators of t-norms on the lattice L\^{ }I of closed subintervals of the unit interval. Starting from a minimal set of axioms that any addition and multiplication operator on L\^{ }I must ful\unmatched{fb01}ll, we investigate the properties of the additive and multiplicative generators on L\^{ }I obtained using these arithmetic operators. We also investigate under which conditions the generators on L\^{ }I generate a t-norm.},
  author       = {Deschrijver, Glad},
  booktitle    = {Proceedings of the 12th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems},
  editor       = {Magdalena, Luis and Ojeda-Aciego, Manuel and Verdegay, Jos{\'e} Luis},
  isbn         = {978-84-612-3061-7},
  language     = {eng},
  location     = {M{\'a}laga, Spain},
  pages        = {1336--1343},
  title        = {Additive generators in interval-valued fuzzy set theory},
  year         = {2008},
}