NEW REVEALED PREFERENCE INDICATORS OF FUZZY CHOICE FUNCTIONS

The axioms WAFRP, SAFRP (resp. WFCA, SFCA) are fuzzy versions of the axioms of revealed preference WARP, SARP (resp. of the congruence axioms WCA, SCA) of classic theory of revealed preference. The revealed preference indicators WAFRP(C), SAFRP(C), WFCA(C) and SFCA(C) of a fuzzy choice function C were introduced in a previous paper in order to express the degree to which C verifies the axioms WAFRP, SAFRP, WFCA, SFCA. In this paper, we shall define the new revealed preference indicators WAFRP°(C), HAFRP(C) corresponding to the axioms WAFRP°, HAFRP from fuzzy revealed preference theory. We shall prove two main results: (1) WAFRP°(C) = WFCA(C); (2) HAFRP(C) = SFCA(C). They extend in terms of numerical indicators two known theorems of Hansson and Suzumura of classic theory of choice functions.