A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components

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.