KU代数上的(∈,∈∨q_((λ,μ)))-模糊正关联理想  

On(∈,∈∨q_((λ,μ)))-Fuzzy Positive Implicative Ideals of KU-Algebras

作　　者：李论[1,2] 廖祖华[1,2,3] 陈柳红[1,2] 宋威[4] 吴树忠 朱晓英[1] LI Lun;LIAO Zuhua;CHEN Liuhong;SONG Wei;WU Shuzhong;ZHU Xiaoying(School of Science, Jiangnan University,Wuxi, Jiangsu 214122, China;Honors School, Jiangnan University,Wuxi, Jiangsu 214122, China;Institute of Intelligence System & Network Computing, Jiangnan University,Wuxi, Jiangsu 214122, China;School of Internet of Things Engineering, Jiangnan University,Wuxi, Jiangsu 214122, China)

机构地区：[1]江南大学理学院,江苏无锡214122 [2]江南大学至善学院,江苏无锡214122 [3]江南大学智能系统与网络计算研究所,江苏无锡214122 [4]江南大学物联网工程学院,江苏无锡214122

出　　处：《计算机科学与探索》2017年第8期1324-1339,共16页Journal of Frontiers of Computer Science and Technology

基　　金：国家自然科学基金Nos.61170121;11401259;61673193;江苏省自然科学基金No.BK20151117;国家大学生创新训练项目No.201610295005~~

摘　　要：给出了KU代数的点态化(∈,∈∨q_((λ,μ)))-模糊正关联理想与广义模糊正关联理想的概念,得到了KU代数的(∈,∈∨q_((λ,μ)))-模糊正关联理想的一些等价刻画,并指出了(∈,∈∨q_((λ,μ)))-模糊正关联理想有丰富的层次结构;其次得到了多个KU代数的(∈,∈∨q_((λ,μ)))-模糊正关联理想的交、并、同态像和同态原像(在一定条件下)也是(∈,∈∨q_((λ,μ)))-模糊正关联理想;而后又对KU代数(∈,∈∨q_((λ,μ)))-模糊正关联理想的直积以及投影进行了研究;最后给出KU代数的正关联理想的降(升)链条件的新概念,并利用(∈,∈∨q_((λ,μ)))-模糊正关联理想的性质研究了KU代数的正关联理想的降(升)链条件。Firstly,this paper gives the concepts of pointwise(∈,∈∨q(λ,μ))-fuzzy positive implicative ideals and generalized fuzzy positive implicative ideals of KU-algebras,obtains some equivalent characterizations of(∈,∈∨q(λ,μ))-fuzzy positive implicative ideals of KU-algebras,and points the richer hierarchical structure of the fuzzy positive implicative ideals.Secondly,this paper acquires the properties that intersections,unions,homomorphic image and homomorphic preimage(under certain condition)of(∈,∈∨q(λ,μ))-fuzzy positive implicative ideals of KU-algebras are also(∈,∈∨q(λ,μ))-fuzzy positive implicative ideals.Then,this paper investigates the direct product and projection of(∈,∈∨q(λ,μ))-fuzzy positive implicative ideals of KU-algebras.At last,this paper introduces the new concepts of the descending(ascending)chain conditions of the positive implicative ideals of KU-algebras,which are studied by using the properties of(∈,∈∨q(λ,μ))-fuzzy positive implicative ideals.

关 键 词：KU代数 (∈ ∈∨q(λ μ))-模糊正关联理想 同态映射 投影 降(升)链条件 

分 类 号：O159[理学—数学]