Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations
给出了弱偏好和严格偏好存在最大元素和极大元素的充要条件，统一了文献中凸性和非循环性两种方法，不要求偏好连续或凸，适用于有序和无序二元关系。
This paper provides necessary and sufficient conditions for the existence of greatest and maximal elements of weak and strict preferences, and unifies two very different approaches used in the related literature (the convexity and acyclicity approaches). Conditions called transfer FS-convexity and transfer SS-convexity are shown to be necessary and, in conjunction with transfer closedness and transfer openness, sufficient for the existence of greatest and maximal elements of weak and strict preferences, respectively. The results require neither the continuity nor convexity of preferences, and are valid for both ordered and unordered binary relations. Thus, the results generalize almost all of the theorems on existence of maximal elements of preferences that appear in the literature.