论文标题
单调的预订空间分类：复杂性和优化
The classification of preordered spaces in terms of monotones: complexity and optimization
论文作者
论文摘要
决策理论中的复杂性和优化的研究涉及在实价单调方面对决策空间的偏好的部分和完整表征。凭借这种动机，并在最近引入了新的单调类（例如注射单调或严格的单调多实量）之后，就实用值单调的存在和基础性而言，我们介绍了预订的空间的分类以及商的基础性空间。特别是，我们利用了对实价单调的表征，以分离增加集合的家族，以获取一个更完整的分类，该分类由彼此严格不同的类别组成。结果，我们获得了对复杂性和优化的新见解，并在预订的空间中阐明了它们的相互作用。
The study of complexity and optimization in decision theory involves both partial and complete characterizations of preferences over decision spaces in terms of real-valued monotones. With this motivation, and following the recent introduction of new classes of monotones, like injective monotones or strict monotone multi-utilities, we present the classification of preordered spaces in terms of both the existence and cardinality of real-valued monotones and the cardinality of the quotient space. In particular, we take advantage of a characterization of real-valued monotones in terms of separating families of increasing sets in order to obtain a more complete classification consisting of classes that are strictly different from each other. As a result, we gain new insight into both complexity and optimization, and clarify their interplay in preordered spaces.
