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On the cartesian product of intuitionistic fuzzy sets

Glad Deschrijver (UGent) and Etienne Kerre (UGent)
(2003) Journal of Fuzzy Mathematics. 11(3). p.537-547
Author
Organization
Abstract
Cartesian products of intuitionistic fuzzy sets have been defined using the min-max and the product-probabilistic sum operations. In this paper we introduce and analyse the properties of a generalized cartesian product of intuitionistic fuzzy sets using a general triangular norm and conorm. In particular we investigate the emptiness, the commutativity, the distributivity, the interaction with respect to generalized unions and intersections, the distributivity with respect to the difference, the monotonicity and the cutting in terms of level-sets.
Keywords
intuitionistic fuzzy set, generalized cartesian product

Citation

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Chicago
Deschrijver, Glad, and Etienne Kerre. 2003. “On the Cartesian Product of Intuitionistic Fuzzy Sets.” Journal of Fuzzy Mathematics 11 (3): 537–547.
APA
Deschrijver, Glad, & Kerre, E. (2003). On the cartesian product of intuitionistic fuzzy sets. Journal of Fuzzy Mathematics, 11(3), 537–547.
Vancouver
1.
Deschrijver G, Kerre E. On the cartesian product of intuitionistic fuzzy sets. Journal of Fuzzy Mathematics. 2003;11(3):537–47.
MLA
Deschrijver, Glad, and Etienne Kerre. “On the Cartesian Product of Intuitionistic Fuzzy Sets.” Journal of Fuzzy Mathematics 11.3 (2003): 537–547. Print.
@article{208230,
  abstract     = {Cartesian products of intuitionistic fuzzy sets have been defined using the min-max and the product-probabilistic sum operations. In this paper we introduce and analyse the properties of a generalized cartesian product of intuitionistic fuzzy sets using a general triangular norm and conorm. In particular we investigate the emptiness, the commutativity, the distributivity, the interaction with respect to generalized unions and intersections, the distributivity with respect to the difference, the monotonicity and the cutting in terms of level-sets.},
  author       = {Deschrijver, Glad and Kerre, Etienne},
  issn         = {1066-8950},
  journal      = {Journal of Fuzzy Mathematics},
  keyword      = {intuitionistic fuzzy set,generalized cartesian product},
  language     = {eng},
  number       = {3},
  pages        = {537--547},
  title        = {On the cartesian product of intuitionistic fuzzy sets},
  volume       = {11},
  year         = {2003},
}