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.
Fono et al.11 characterized, for an intuitionistic fuzzy t-norm [Formula: see text], two properties of a given regular intuitionistic fuzzy strict component of a (T,S)-transitive intuitionistic fuzzy preference. In this paper, we examine these characterizations in the particular case where [Formula: see text]. We then use these (general and particular) results to obtain some intuitionistic fuzzy versions of Arrow's impossibility theorem. Therefore, by weakening a requirement to social preferences, we deduce a positive result, that is, we display an example of a non-dictatorial Intuitionistic Fuzzy Agregation Rule (IFAR) and, we establish an intuitionistic fuzzy version of Gibbard's oligarchy theorem.
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