International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 580918, 38 pages
doi:10.1155/2009/580918
A binary intuitionistic fuzzy relation: some new results, a general factorization, and two properties of strict components
Louis Aimé Fono1
, Gilbert Njanpong Nana2
, Maurice Salles3
and Henri Gwet4
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
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.