International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 580918, 38 pages
doi:10.1155/2009/580918
Research Article
A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components
1Département de Mathématiques et Informatique, Faculté des Sciences, Université de Douala, B.P. 24157 Douala, Cameroon
2Laboratoire de Mathématiques Appliquées aux Sciences Sociales, Département de Mathématiques, Faculté des Sciences, Université de Yaoundé I, B.P. 15396 Yaoundé, Cameroon
3MRSH, University of Caen, CREM-UMR 6211, CNRS, 14032 Caen Cedex, France
4Department of Mathematics, National Polytechnic Institute, P.O. Box 8390, Yaoundé, Cameroon
Received 3 July 2008; Revised 24 December 2008; Accepted 15 June 2009
Academic Editor: Andrzej Skowron
Copyright © 2009 Louis Aimé Fono et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We establish, by means of a large class of
continuous t-representable intuitionistic fuzzy t-conorms, a factorization of an intuitionistic fuzzy relation (IFR) into a
unique indifference component and a family of regular strict components. This result generalizes a previous factorization
obtained by Dimitrov (2002) with the (max,min)
intuitionistic fuzzy t-conorm. We provide, for a continuous
t-representable intuitionistic fuzzy t-norm 𝒯, a characterization of the 𝒯-transitivity of an IFR. This enables us to determine necessary and sufficient conditions on a
𝒯-transitive IFR R under which a strict component of
R satisfies pos-transitivity and negative transitivity.