On relationships between numerical representations of interval orders and semiorders (Q1099050)

The extent to which continuous numerical repesentations of interval orders are unique is considered. A pair of continuous, real-valued functions \(<u,v>\), represents an interval order, \(<X,\succ >\), provided that for x,y\(\in X\), \(x\succ y\) 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 continues representation can be derived from another is described. Similar considerations are made for special forms of continuous numerical representations of semiorders.