Fuzzy arrow-type results without the Pareto principle based on fuzzy pre-orders

In this paper, we introduce appropriate properties of fuzzy preferences and fuzzy aggregation rules. We use them to provide fuzzy counterparts of Malawski and Zhou's [A note on social choice theory without the pareto principle, Social Choice and Welfare 16 (1994)] and Wilson's [Social choice theory without the pareto principle, Journal of Economic Theory 5 (1972) 478–486] impossibility results concerning the aggregation of individual preferences, which do not assume the Pareto principle. By weakening conditions on fuzzy social preferences, we obtain a possibility result.