Revealed Fuzzy Preferences

It is proved that there is a one-to-one mapping between the class of all antireflexive binary nonfuzzy relations and a class of choice functions with special properties. The direct mapping is the rule of choice, the inverse mapping is the revealed preference. A fuzzy extension of these notions are given showing this result also holds for fuzzy choice on nonfuzzy sets i.e. for fuzzy preferences. Because the properties of choice functions allow for a trivial fuzzy extension, it is convinient to describe properties of fuzzy relations in terms of choice functions, i.e. to consider the revealed fuzzy preferences. The above principle of fuzzy extension is applied to a fuzzy multiperson choice problem.