Generalized manipulability of fuzzy social choice functions

In many social decision making contexts, a manipulator attempts to change the social choice in his favor by misrepresenting his preferences. This paper deals with the strategic manipulation problem of social choice functions aggregating fuzzy individual preferences. It defines how the strategic misrepresentation of fuzzy preferences can be profitable for an individual with a fuzzy weak preference relation. The case of max-inverted perpendicular-transitive fuzzy preference relations is considered where inverted perpendicular is a t-norm. Then, the impossibility of building a non-manipulable fuzzy social choice function except the dictatorial one is established, generalizing thus the well-known Gibbard-Satterthwaite's result. The obtained results generalizes also the one of Ben Abdelaziz et al. for max-min transitive fuzzy preference relations.