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On the relationship between arithmetic operators and t-norms in interval-valued fuzzy set theory

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Organization
Abstract
In this paper we study extensions of the arithmetic operators +, −, ·, ÷ to the lattice L^I of closed subintervals of the unit interval. Starting from a minimal set of axioms that these operators must fulfill, we investigate which properties they satisfy. We also investigate some classes of t-norms on L^I which can be generated using these operators.
Keywords
interval-valued fuzzy set, arithmetic operators, t-norm

Citation

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Chicago
Deschrijver, Glad. 2007. “On the Relationship Between Arithmetic Operators and T-norms in Interval-valued Fuzzy Set Theory.” In Proceedings of the Fourth International Summer School on Aggregation Operators, ed. Bernard De Baets, Koen Maes, and Radko Mesiar, 185–191. Academia Press.
APA
Deschrijver, Glad. (2007). On the relationship between arithmetic operators and t-norms in interval-valued fuzzy set theory. In Bernard De Baets, K. Maes, & R. Mesiar (Eds.), Proceedings of the Fourth International Summer School on Aggregation Operators (pp. 185–191). Presented at the 4th International Summer School on Aggregation Operators (AGOP 2007), Academia Press.
Vancouver
1.
Deschrijver G. On the relationship between arithmetic operators and t-norms in interval-valued fuzzy set theory. In: De Baets B, Maes K, Mesiar R, editors. Proceedings of the Fourth International Summer School on Aggregation Operators. Academia Press; 2007. p. 185–91.
MLA
Deschrijver, Glad. “On the Relationship Between Arithmetic Operators and T-norms in Interval-valued Fuzzy Set Theory.” Proceedings of the Fourth International Summer School on Aggregation Operators. Ed. Bernard De Baets, Koen Maes, & Radko Mesiar. Academia Press, 2007. 185–191. Print.
@inproceedings{376991,
  abstract     = {In this paper we study extensions of the arithmetic operators +, \ensuremath{-}, {\textperiodcentered}, {\textdiv} to the lattice L\^{ }I of closed subintervals of the unit interval. Starting from a minimal set of axioms that these operators must ful\unmatched{fb01}ll, we investigate which properties they satisfy. We also investigate some classes of t-norms on L\^{ }I which can be generated using these operators.},
  author       = {Deschrijver, Glad},
  booktitle    = {Proceedings of the Fourth International Summer School on Aggregation Operators},
  editor       = {De Baets, Bernard and Maes, Koen and Mesiar, Radko},
  isbn         = {978-90-382-1140-4},
  language     = {eng},
  location     = {Gent, Belgium},
  pages        = {185--191},
  publisher    = {Academia Press},
  title        = {On the relationship between arithmetic operators and t-norms in interval-valued fuzzy set theory},
  year         = {2007},
}