形式无约束下偏好集映射、拓扑交和一致性

该文采用集映射刻画偏好序,并采用拓扑交运算刻画标度偏好序的共识、一致性等概念,以及刻画其基本特征.在序理论的广阔体系上,聚焦于偏好序构造的基本体系,即共识运算存在性、偏好序完全性、拓扑交严格性特征、偏好序分解的拓扑交,并获得了基本结论,在基础层面上为序拓扑理论及其构造性应用提供了逻辑支撑.同时,严格采用拓扑交以体系化编撰偏好序的重要方面,将为偏好序的“一致性研究”后续拓扑加载提供广阔的空间.

The Set-Valued Map of Preference,Topology-Intersection and Consistency under No Constraints

In this paper,the set mapping is used to describe the preference order,and the topological intersection is used to describe the concepts of consensus and consistency of the scale preference order,and its basic characteristics are described.On the broad system of order theory,it focuses on the basic system of preference order construction,that is,the existence of consensus operations,the completeness of preference order,the strict topological intersection feature,and the topological intersection of preference order decomposition,and basic conclusions are obtained.It provides logical support for ordered topology theory and its constructive applications.At the same time,the strict use of topological intersection to systematically compile important aspects of preference order will provide a broad space for subsequent topological loading of preference order "consistency research".