On fuzzy non-discrimination

We show that the incompatibility between the Pareto principle and the notion of non-discrimination as presented in Xu (2000) continues to hold when the individuals have exact preferences and the social preference relation is allowed to be a reflexive and transitive fuzzy binary relation. Our result can be seen as a strengthening of the result of Xu in two directions: (1) the range of the aggregation rule is enlarged and (2) a weaker condition on non-discrimination is used.