doi:10.1155/2009/580918 Research Article A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components

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-normT, a characterization of theT-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. Copyright q 2009 Louis Aime ́ 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. 1