Strategic manipulation and regular decomposition of fuzzy preference relations

Ben Abdelaziz et al. (2008) have shown that any non-dictatorial fuzzy social choice function is vulnerable to strategic manipulation, when individuals express their preferences trough fuzzy weak relations on the set of alternatives. This paper proposes a new definition of fuzzy manipulability and dictatorship of fuzzy social choice functions. For this purpose, the decomposition of fuzzy weak relations in terms of symmetric and regular components is considered and a parallel result is provided. The proof is done by induction on the number of individuals.