软完全正则子半群  

Soft Completely Regular Sub-semigroups

作　　者：叶灵军[1] 廖祖华[1] 朱晓英[1] 赵迪[1] 

机构地区：[1]江南大学理学院,江苏无锡214122

出　　处：《工程数学学报》2014年第3期341-346,共6页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11001109);江苏省教育科学"十一五"规划项目(D/2006/01/171);江南大学创新团队发展计划资助项目(应用数学200902);江南大学大学生创新训练计划项目(2011-596)~~

摘　　要：Molodstov提出的软集理论是解决不确定性问题的一种有效的数学工具.本文首先在软集的基础上,将参数集赋予完全正则半群的代数结构,给出了软完全正则子半群的新概念,得到了它的一些等价刻画;其次,利用软集的交和且运算,论证了软完全正则子半群的交和且运算也是软完全正则子半群;最后,应用对偶软集的方法研究了软完全正则子半群和对偶软集之间的关系,获得了它们的一些性质.Molodtsov introduced the theory of soft sets,which can be used as an effectively mathematical tool for dealing with vagueness.In this paper,based on soft sets,we firstly assign the parameter sets a algebraic structure of completely regular semigroups and introduce the concept of soft completely regular sub-semigroups.Then,their equivalent characterizations are obtained.Next,by using the intersection and the and operation of soft sets,we show that the intersection and the and operation of soft completely regular sub-semigroups are also soft completely regular sub-semigroups.Finally,by using the dual soft sets,we study the relationship between the soft completely regular sub-semigroup and its dual soft set and get some properties of them.

关 键 词：软集 对偶软集 软集的交运算 软集的且运算 软完全正则子半群 

分 类 号：O144.1[理学—数学] O159[理学—基础数学]