Abstract
The extent to which continuous numerical representations of interval orders are unique is considered. Apair of continuous, real-valued functions, < u, v>, represents an interval order, < X, >>, 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.
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