集映射、拓扑交和对影序的存在性  

Set-valued order,topology-intersection and the existence of back projection

作　　者：卢美华[1] 高晓波 LU Meihua;GAO Xiaobo(School of Science,Jiangxi University of Technology,Nanchang 330022,China;College of Computer and Information Engineering,Jiangxi Agricultural University,Nanchang 330045,China)

机构地区：[1]江西科技学院理科部,江西南昌330022 [2]江西农业大学计算机与信息工程学院,江西南昌330045

出　　处：《南昌大学学报（理科版）》2023年第4期317-322,327,共7页Journal of Nanchang University(Natural Science)

基　　金：江西省文化科学规划资助(YG2022184);国家社科基金资助项目(17BJL025)。

摘　　要：以集映射刻画序关系,提出并以无条件性拓扑交刻画社会选择函数“逆向构造”的对影序,以拓扑交构造对影序,以拓扑交刻画对影的部分性质,并特别刻画了集序等价族分解的全部特征,对影中左、右分影能达到序向严格化,并给出了对影存在性的构造性证明。从而,偏好集结中以拓扑交构造的序关系能够严格形式化,本质上还可联系孔多塞循环和轮换。从框架的可拓性上,考虑无条件性拓扑交的约束公理加载,形成序关系拓扑体系的完整框架,具有重要理论意义。The order relation was described by set-valued mapping,and an unconditional topological intersection was proposed to characterize the anti-shadow order of the social choice function“reverse construction”.All the characteristics of the decomposition of the set-order equivalence family can achieve the strict ordering of the left and right shadows in the shadow,and a constructive proof of the existence of the shadow was given.Therefore,the order relation constructed by topological intersection in preference aggregation can be strictly formalized,and it can also be related to Condorcet cycle and rotation in essence.From the extension of the frame,it was of great theoretical significance to consider the constraint axiom loading of the unconditional topological intersection to form a complete frame of the topological system of order relation.

关 键 词：集序 对影 拓扑交 

分 类 号：O225[理学—运筹学与控制论] C934[理学—数学]