Strategy-proof fuzzy aggregation rules

We investigate the structure of fuzzy aggregation rules which, for every permissible profile of fuzzy individual preferences, specify a fuzzy social preference. We show that all fuzzy aggregation rules which are strategy-proof and satisfy a minimal range condition are dictatorial. In other words, there is an individual whose fuzzy preferences determine the entire fuzzy social ranking at every profile in the domain of the aggregation rule. To prove this theorem, we show that all fuzzy aggregation rules which are strategy-proof and satisfy the minimal range condition must also satisfy counterparts of independence of irrelevant alternatives and the Pareto criterion. There has been hardly any treatment of the manipulability problem in the literature on social choice with fuzzy preferences.