计算机科学与探索 ›› 2017, Vol. 11 ›› Issue (8): 1324-1339.DOI: 10.3778/j.issn.1673-9418.1703085

• 理论与算法 • 上一篇    下一篇

KU 代数上的( ∈,∈∨q(λ,μ)) -模糊正关联理想

李  论1,2,廖祖华1,2,3+,陈柳红1,2,宋  威4,吴树忠1,朱晓英1   

  1. 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
  • 出版日期:2017-08-01 发布日期:2017-08-09

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

LI Lun1,2, LIAO Zuhua1,2,3+, CHEN Liuhong1,2, SONG Wei4, WU Shuzhong1, ZHU Xiaoying1   

  1. 1. School of Science, Jiangnan University, Wuxi, Jiangsu 214122, China
    2. Honors School, Jiangnan University, Wuxi, Jiangsu 214122, China
    3. Institute of Intelligence System & Network Computing, Jiangnan University, Wuxi, Jiangsu 214122, China
    4. School of Internet of Things Engineering, Jiangnan University, Wuxi, Jiangsu 214122, China
  • Online:2017-08-01 Published:2017-08-09

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。

关键词: KU代数, ( &isin, &isin, &or, q(&lambda, , &mu, )) -模糊正关联理想, 同态映射, 投影, 降(升)链条件

Abstract:  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.

Key words: KU-algebras;( ∈,∈∨q(λ,μ)) -fuzzy positive implicative ideals, homomorphic mapping, projection, des-cending (ascending) chain condition