Existence of maximal points with respect to ordered bipreference relations (Q1176846)

A generalization of the maximality of a point with respect to preference relations, which are not assumed to be partial orders, is introduced. So, the notions of \((s,r)\)-maximality and \((s,r)\)-domination are defined, where \((s,r)\) is an ordered pair of preference relations. The authors show three possible techniques of investigating the maximality with respect to a given pair of relations, named scalarization, approximation and duality and give general necessary and sufficient conditions for the existence of \((s,r)\)-maximal points in a given set. They also show by comparison of some of these conditions with those of \textit{H. W. Corley, G. B. Hazen} and \textit{T. L. Morin} [ibid. 40, 26-60 (1983; Zbl 0488.90064)], and by illustrative examples, the generality of their results.