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Numerical representability of semiorders

2002; Elsevier BV; Volume: 43; Issue: 1 Linguagem: Inglês

10.1016/s0165-4896(01)00082-8

1879-3118

Juan C. Candeal, Esteban Induráin, Margarita Zudaire,

Logic, Reasoning, and Knowledge

In the framework of the analysis of orderings whose associated indifference relation is not necessarily transitive, we study the structure of a semiorder, and its representability through a real-valued function and a threshold. Inspired in a recent characterization of the representability of interval orders, we obtain a full characterization of the existence of numerical representations for semiorders. This is an extension to the general case of the classical Scott–Suppes theorem concerning the representability of semiorders defined on finite sets.