What kind of preference maximization does the weak axiom of revealed non-inferiority characterize?

A choice correspondence is weak justified if a non-chosen alternative is dominated by any other obtainable alternative, and for each discarded alternative there is some chosen alternative which dominates it. This definition allows us to build a connection between the behavioral property expressed by the weak axiom of revealed non-inferiority and a weak form of maximality. It is weaker than the form of maximality characterized by the weak axiom of revealed preference