The elaboration of preference relations and their representations trace their source to early economic theory. Classical representations of preferences theorems rely on Debreu–Eilenberg’s theorems in the topological setting. An important class of preferences consists of interval orders. A natural question is to achieve a bi-utility representation for interval orders. We suggest to introduce a condition reminiscent of N. Wiener’s early works on the relativeness of positions. We obtain a bi-utility representation through the precedence and succession relations.

中文翻译：

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通过双效用函数表示区间顺序

偏好关系及其表示的详细阐述可追溯到早期的经济理论。偏好定理的经典表示依赖于拓扑设置中的 Debreu-Eil​​enberg 定理。一类重要的偏好包括区间订单。一个自然的问题是实现区间订单的双效用表示。我们建议引入一个让人想起 N. Wiener 关于位置相对性的早期著作的条件。我们通过优先级和继承关系获得了双效用表示。