亚BCI-代数的新型软正关联理想  

New type of soft positive implicative ideals of weak-BCI-algebras

作　　者：黄昱[1] 廖祖华[2] 李论 HUANG Yu;LIAO Zuhua;LI Lun(School of Basic Education,Taihu University of Wuxi,Wuxi,Jiangsu 214064,China;School of Science,Jiangnan University,Wuxi,Jiangsu 214122,China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]无锡太湖学院基础教育学院,江苏无锡214064 [2]江南大学理学院,江苏无锡214122 [3]中国科学院数学与系统科学研究院,北京100190

出　　处：《计算机工程与应用》2018年第21期31-36,共6页Computer Engineering and Applications

基　　金：国家自然科学基金(No.61170121);江苏省自然科学基金(No.BK20151117);无锡太湖学院自然科学基金(No.16WUNS006)

摘　　要：给出了亚BCI-代数正关联理想的概念,讨论了亚BCI-代数正关联理想与理想的关系。将软集的参数集赋予亚BCI-代数,提出了亚BCI-代数新型软正关联理想的概念,举例说明了它与通常的软正关联理想不同。研究了亚BCI-代数新型软正关联理想与新型软理想之间的关系,讨论了亚BCI-代数新型软正关联理想在软集运算下的运算性质,最后分别利用对偶软集和软集的水平集,给出了亚BCI-代数新型软正关联理想与正关联理想之间的等价刻画。The notion of positive implicative ideals of weak-BCI-algebras is introduced,and the relationship between positive implicative ideals and ideals is discussed.By endowing a parameter set as a weak-BCI-algebra,the definition of a new type of soft positive implicative ideals of weak-BCI-algebras is proposed.Examples are given to show that it is different from common soft positive implicative ideals.Relationship between a new type of soft positive implicative ideals and soft ideals is discussed.By using operations of two soft sets,some properties of a new type of soft positive implicative ideals of Weak-BCI-algebras are obtained.Finally,by applying the dual soft sets and level set of soft set,the equivalent characterizations of a new type of soft ideals of weak-BCI-algebras are given.

关 键 词：亚BCI-代数 软集 新型软正关联理想 对偶软集 水平集 

分 类 号：O159[理学—数学]