Consistency indicators for fuzzy choice functions

For a fuzzy choice function C we study two consistency indicators Fα(C), Fβ(C) and a congruence indicator WFCA(C). The indicators Fα(C) and Fβ(C) express the degree to which C verifies the extension to the fuzzy case of Sen's conditions α and β, while WFCA(C) evaluates the degree to which C verifies the weak fuzzy congruence axiom WFCA. The main result of the paper shows that WFCA(C) is the minimum of Fα(C) and Fβ(C). The three indicators can be used for obtaining a hierarchy of a class of fuzzy choice functions.