On relationships between numerical representations of interval orders and semiorders
Abstract The extent to which continuous numerical representations of interval orders are unique is considered. Apair of continuous, real-valued functions, , represents an interval order, >, provided that for x, y ϵ X, x > y if and only if u(x) > v(y). Relationships which necessarily hold between any two such numerical representations are presented and a method by which one continuous representation can be derived from another is described. Similar considerations are made for special forms of continuous numerical representations of semiorders.