Vague软Clifford半群  

Vague Soft Clifford Semigroup

作　　者：于晓丹 孔祥智[1] YU Xiao-dan;KONG Xiang-zhi(School of Science,Jiangnan University,Wuxi Jiangsu 214122,China)

机构地区：[1]江南大学理学院,江苏无锡214122

出　　处：《西南大学学报（自然科学版）》2020年第6期46-53,共8页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11371174,11301227).

摘　　要：Vague软集融合了Vague集和软集的优点,是一种处理不确定性问题的重要工具,关于它的代数结构的研究有很多.Clifford半群是一种完全正则半群,它是逆半群中很特殊也很重要的一个类别.基于Vague软集和Clifford半群的现有理论知识,首次将Vague软集和Clifford半群相结合,把Clifford半群模糊化,提出新概念Vague软Clifford半群,它是Vague软集的一个新代数结构,接着给出了Vague软Clifford半群的等价性和Vague软Clifford子半群的定义,并研究了Vague软Clifford半群的基本代数性质.首先,证明了:任意两个Vague软Clifford半群的交集、并集仍是Vague软Clifford半群.其次,证明了:Vague软Clifford半群是群的半格且是群的强半格,并且它是正则半群,给出了Vague软Clifford半群的半群结构分解.最后,给出了两个Vague软Clifford半群间的同态定义,并且验证了Vague软Clifford半群之间的同态关系.Vague soft set combines the advantages of Vague set and soft set,it is an important tool for dealing with the problem of uncertainty.There are many studies on its algebraic structure.Clifford semigroup is a completely regular semigroup,it is a very special and important category in inverse semigroups.Based on the existing theoretical knowledge of Vague soft sets and Clifford semigroups,Vague soft sets and Clifford semigroups are combined to blur the Clifford semigroups for the first time,and a new concept Vague soft Clifford semigroup is proposed.It is a new algebraic structure of Vague soft set.Then the equivalence of Vague soft Clifford semigroups and the definition of Vague soft Clifford subsemigroups are given,and the basic algebraic properties of Vague soft Clifford semigroups are studied.Firstly,it is proved that the intersection and the union of any two Vague soft Clifford semigroups remain to be Vague soft Cliffford semigroups.Secondly,it is proved that the Vague soft Clifford semigroup is a semilattice of a group and a strong semilattice of the group and it is a regular semigroup.The semigroup structural decomposition of the Vague soft Clifford semigroup is given.Finally,the definition of homomorphism between two Vague soft Clifford semigroups is given,and the homomorphic relationship between Vague soft Clifford semigroups is verified.

关 键 词：Vague软集 CLIFFORD半群 Vague软Clifford半群 半群同态 

分 类 号：O159[理学—数学]