偏序集的软理想  

Soft Ideals of Posets

作　　者：梁世欣 郝旭东[1] Liang Shixin;Hao Xudong(Department of Philosophy,East China Normal University,Shanghai 200241,China)

机构地区：[1]华东师范大学哲学系,上海200241

出　　处：《洛阳师范学院学报》2021年第8期4-9,共6页Journal of Luoyang Normal University

基　　金：国家社会科学基金一般项目(15BZX085)。

摘　　要：偏序集的理想在偏序集理论乃至在格论的研究中都起着十分重要的作用,而软集理论及其应用又在处理不确定性问题中有着巨大的潜力.故而将软集理论与偏序集的理想相结合,引入了偏序集的软理想的概念,得到了软理想的软子集、两个软理想的扩展交、且以及直积等仍为软理想.并以此为基础讨论了两个软理想在一定条件下的限制差是软理想.最后给出了偏序软同构的概念并证明了软理想的偏序软同构的像仍为软理想.The concepts of ideals on posets play a very important role in the poset theory and lattice theory.And the soft set theory and its application have a great potential in dealing with uncertainty.In this light,the concept of soft ideals of posets is firstly introduced combining the soft set theory with the ideal of posets,and then a soft subset of a soft ideal,the extended intersection of two soft ideals are got,and its direct product is still a soft ideal.Furthermore,it is discussed that under certain conditions,the restricted difference of two soft ideals is a soft ideal.Finally the concept of partial order soft isomorphism is presented and it is proved that the image of partial order soft isomorphism of a soft ideal is still a soft ideal.

关 键 词：偏序集的理想 软集 软集运算 同构映射 

分 类 号：O153.1[理学—数学]