Consistency Conditions in Fuzzy Consumers Theory

Abstract

This paper is concerned with consistency properties for fuzzy consumers. We introduce the consistency conditions Fα, Fβ, Fδ as fuzzy forms of Sen's properties alpha, beta and delta. Other consistency conditions are also studied: Fα2, Fβ(+), Fγ2 and FPI. The main results are:

(1) A fuzzy consumer verifies Fα, Fβ if and only if the congruence axiom WFCA holds;

(2) If h is a normal fuzzy consumer then Fδ holds if and only if the associated fuzzy preference relation R is quasi-transitive;

(3) A fuzzy consumer is normal if and only if conditions Fα2, Fγ2 hold.