FUZZY CHOICE FUNCTIONS, REVEALED PREFERENCE AND RATIONALITY

This paper investigates the conditions under which a fuzzy-set-valued choice function is rationalisable by a fuzzy revealed preference relation satisfying certain regularity conditions. Attention is confined to the case where the domain of the choice function consists of all (crisp) finite subsets of the universal set of alternatives, Two sets of weak and strong axioms of fuzzy revealed preference (WAFRP and SAFRP) are stated. In both cases it turns out that WAFRP is not equivalent to SAFRP and that SAFRP does not characterise rationality. In the special case where every set of available alternatives has at least one element which is unambiguously chosen, WAFRP is equivalent to SAFRP but SAFRP still does not characterise rationality. A fuzzy congruence condition, stronger than SAFRP, is proposed and is shown to be necessary and sufficient for rationality.