Fuzzy strict preference and social choice

In this paper we generalize some classical factorizations of a fuzzy relation into a symmetric component (indifference) and an asymmetric and regular component (regular fuzzy strict preference). From the above notions, we establish two properties of any regular fuzzy strict preference of a max-*-transitive fuzzy relation, which are then used to obtain new fuzzy versions of Gibbard's oligarchy theorem and Arrow's impossibility theorem.