模糊偏序集中模糊子集的上下确界能否定义为模糊点  

Can we Define Fuzzy Points to be the Joins/Meets of Fuzzy Subsets of Fuzzy Posets?

作　　者：路玲霞 赵蕾[1] 姚卫 LU Ling-xia;ZHAO Lei;YAO Wei(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《模糊系统与数学》2024年第1期81-87,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金项目重点项目(批准号:12231007);国家自然科学基金项目面上项目(批准号:12371462);江苏省“双创人才”项目(JSSCRC202521).

摘　　要：模糊序理论(又称为量化序理论)是近年来模糊数学的一个研究热点,在模糊拓扑学、模糊domain理论、模糊粗糙集理论和模糊概念格理论中具有重要作用.本文尝试寻找如下问题的解答:模糊偏序集中模糊子集的上下确界能否定义为模糊点?结论表明,这种想法几乎无法成功实现.Fuzzy order theory(also called quantitative order theory)is a hot point in the study of theoretical aspect of fuzzy mathematics,which has important applications in fuzzy topology,fuzzy domain theory,fuzzy rough set theory and fuzzy formal concept analysis,etc.This paper aims to make an attempt to find the solution of the question that can we define fuzzy points to be the suprema/infima of fuzzy subsets of a fuzzy poset?Unfortunately,results show that the idea can seldom be successful.

关 键 词：模糊偏序集 上确界 下确界 模糊点 

分 类 号：O159[理学—数学]