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On the composition of intuitionistic fuzzy relations

Glad Deschrijver and Etienne Kerre UGent (2003) Fuzzy Sets and Systems. 136(3). p.333-361
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
intuitionistic fuzzy set, fuzzy relation, intuitionistic fuzzy relation, triangular composition
journal title
Fuzzy Sets and Systems
Fuzzy Sets Syst.
volume
136
issue
3
pages
333-361 pages
Web of Science type
Article
Web of Science id
000183237400005
JCR category
MATHEMATICS, APPLIED
JCR impact factor
0.577 (2003)
JCR rank
85/153 (2003)
JCR quartile
3 (2003)
ISSN
0165-0114
language
English
UGent publication?
yes
classification
A1
id
208228
handle
http://hdl.handle.net/1854/LU-208228
date created
2008-01-11 10:41:00
date last changed
2016-12-19 15:39:15
@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},
}

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.