A complementary approach to transitive rationalizability

In this article, we study the axiomatic foundations of revealed preference theory. We define two revealed relations from the weak and strong revealed preference. The alternative x is preferred to y with respect to U if x, being available in an admissible set implies, the rejecting of y; and x is preferred to y with respect to Q if the rejecting of x implies the rejecting of y. The purpose of the paper is to show that the strong axiom of revealed preference and Hansson's axiom of revealed preference can be given with the help of U and Q and their extension properties.