Consistency indicators for fuzzy choice functions

For a fuzzy choice function C we study two consistency indicators F-alpha(C), F-beta(C) and a congruence indicator WFCA(C). The indicators F-alpha(C) and F-beta(C) express the degree to which C verifies the extension to the fuzzy case of Sen's conditions alpha and beta, 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 F-alpha(C) and F-beta(C). The three indicators can be used for obtaining a hierarchy of a class of fuzzy choice functions. (c) 2006 Elsevier B.V. All rights reserved.