Arrow-Type Results Under Intuitionistic Fuzzy Preferences

Abstract

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.

Factorization of Intuitionistic Fuzzy Preference Relations

“…In Ref. 7, the authors obtained some intuitionistic versions of Arrow's impossibility theorem. They also provide an example of a nondictatorial intitionistic fuzzy aggregation rule.…”