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On the composition of intuitionistic fuzzy relations

Glad Deschrijver (UGent) and Etienne Kerre (UGent)
(2003) Fuzzy Sets and Systems. 136(3). p.333-361
Author
Organization
Abstract
Fuzzy relations are able to model vagueness, in the sense that they provide the degree to which two objects are related to each other. However, they cannot model uncertainty: there is no means to attribute reliability information to the membership degrees. Intuitionistic fuzzy sets, as defined by Atanassov, give us a way to incorporate uncertainty in an additional degree. Intuitionistic fuzzy relations are intuitionistic fuzzy sets in a cartesian product of universes. One of the main concepts in relational calculus is the composition of two relations. Burillo and Bustince have extended the sup-T composition of fuzzy relations to a composition of intuitionistic fuzzy relations. In this paper, we present an intuitionistic fuzzy version of the triangular compositions of Bandler and Kohout and the variants of these compositions given by De Baets and Kerre. Some properties of these compositions are investigated: containment, convertibility, monotonicity, interaction with union and intersection.
Keywords
intuitionistic fuzzy set, fuzzy relation, intuitionistic fuzzy relation, triangular composition

Citation

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Chicago
Deschrijver, Glad, and Etienne Kerre. 2003. “On the Composition of Intuitionistic Fuzzy Relations.” Fuzzy Sets and Systems 136 (3): 333–361.
APA
Deschrijver, Glad, & Kerre, E. (2003). On the composition of intuitionistic fuzzy relations. Fuzzy Sets and Systems, 136(3), 333–361.
Vancouver
1.
Deschrijver G, Kerre E. On the composition of intuitionistic fuzzy relations. Fuzzy Sets and Systems. 2003;136(3):333–61.
MLA
Deschrijver, Glad, and Etienne Kerre. “On the Composition of Intuitionistic Fuzzy Relations.” Fuzzy Sets and Systems 136.3 (2003): 333–361. Print.
@article{208228,
  abstract     = {Fuzzy relations are able to model vagueness, in the sense that they provide the degree to which two objects are related to each other. However, they cannot model uncertainty: there is no means to attribute reliability information to the membership degrees. Intuitionistic fuzzy sets, as defined by Atanassov, give us a way to incorporate uncertainty in an additional degree. Intuitionistic fuzzy relations are intuitionistic fuzzy sets in a cartesian product of universes. One of the main concepts in relational calculus is the composition of two relations. Burillo and Bustince have extended the sup-T composition of fuzzy relations to a composition of intuitionistic fuzzy relations. In this paper, we present an intuitionistic fuzzy version of the triangular compositions of Bandler and Kohout and the variants of these compositions given by De Baets and Kerre. Some properties of these compositions are investigated: containment, convertibility, monotonicity, interaction with union and intersection.},
  author       = {Deschrijver, Glad and Kerre, Etienne},
  issn         = {0165-0114},
  journal      = {Fuzzy Sets and Systems},
  keyword      = {intuitionistic fuzzy set,fuzzy relation,intuitionistic fuzzy relation,triangular composition},
  language     = {eng},
  number       = {3},
  pages        = {333--361},
  title        = {On the composition of intuitionistic fuzzy relations},
  volume       = {136},
  year         = {2003},
}

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