An interval order ≺ defined on X is said to be representable if there exist two real-valued functions u,v:X→ R such that u(x)≤v(x) and x≺y⇔v(x)<u(y) (x,y∈X) .

We are interested in finding representations for a semiorder ≺, defined on a set X, whose associated indifference ∼ is not transitive. (If ∼ were transitive, by ...

Mar 10, 2012 · We introduce a codomain to represent semiorders, total preorders and interval orders by means of a single map.

Introduction. Interval orders are perhaps the best class of ordered structures to build models of uncertainty or to represent.

This is an extension to the general case of the classical Scott–Suppes theorem concerning the representability of semiorders defined on finite sets.

"Numerical representability of semiorders," Mathematical Social Sciences, Elsevier, vol. 43(1), pages 61-77, January. Handle: RePEc:eee:matsoc:v:43:y:2002:i ...

Mar 10, 2012 · The present paper continues the analysis initiated in [2, 4, 6, 7]. We study the exis- tence of representations of orderings defined on a ...

We introduce a codomain to represent semiorders, total preorders and interval orders by means of a single map. We characterize the semiorders that are ...

A semiorder is a type of ordering for items with numerical scores, where items with widely differing scores are compared by their scores.

Dec 16, 2021 · This paper proposes a new proof of the existence of constant threshold repre- sentations of semiorders on countably infinite sets.