Fuzzy choice functions, revealed preference and rationality

Fuzzy and probabilistic choice functions: a new set of rationality conditions

“…In fact, while fuzzy choice functions have been widely studied, it is still not clear how they can be observed in real situations. We agree with Banerjee [5] when he says that "[...] there may be problems of estimation, but fuzzy choice functions are, in theory, observable". With the proposed method we can rely on probabilistic choice functions, which are much easier to observe: they can be estimated by using the frequency of choice of an element in a set of alternatives, in a data set of repeated observations of choices on the same set of alternatives.…”

“…The same situation appeared in the framework of fuzzy choice theory and in the last years this gap has been filled with comprehensive studies on the connections between fuzzy and classical choice theory (see, amongst others, [5,13,16,17,21,28,29]). Surprisingly, there appears to be no literature on the comparison between fuzzy and probabilistic choice theory.…”

“…Fuzzy choice theory has been proposed first by Banerjee [5] and further corrected and extended by Wang [28]. They develop a theory of choice where both preferences and choice functions are allowed to be fuzzy.…”

“…The second approach exploits the fact that imprecise situations can be conveniently described by means of fuzzy concepts, in which statements such as "x is preferred to y" or "x is the chosen element from the set of alternatives S" can be associated to a certain degree of truth. Fuzzy choice theory [5,13,17], contrary to probabilistic choice theory, does not assumes that the behaviour of individuals is "fuzzy" in nature, but simply profits the modelling power of fuzzy set theory to accommodate for those situations in which choice and preference cannot be described in the classical way.…”

Bridging Probabilistic and Fuzzy Approaches to Choice Under Uncertainty

“…In the last years the results of classical (crisp) revealed choice theory have been extended to the fuzzy framework, laying bare the connections between fuzzy preference relations and fuzzy choice functions (see, amongst others, [2,3,7,10,11,12,14,20,21]). Surprisingly, while the connection between fuzzy preference relations and fuzzy choice functions has been studied in depth, there appears to be no literature on the comparison of fuzzy choice functions and probabilistic choice functions.…”