Journal of Frontiers of Computer Science and Technology ›› 2013, Vol. 7 ›› Issue (11): 1048-1056.DOI: 10.3778/j.issn.1673-9418.1307023

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 (∈,∈∨q(λ,μ))-Fuzzy Ideal of N(2,2,0) Algebra

ZHANG Jianzhong1, FU Xiaobo1,2,3, LIAO Zuhua2,3+   

  1. 1. Section of Foundation Education, Wuxi Institute of Technology, Wuxi, Jiangsu 214121, China
    2. School of Science, Jiangnan University, Wuxi, Jiangsu 214122, China
    3. Engineering Research Center of Internet of Things Technology Application of Ministry of Education, Jiangnan University, Wuxi, Jiangsu 214122, China
  • Online:2013-11-01 Published:2013-11-04

N(2,2,0)代数的(∈,∈∨q(λ,μ))-模糊理想

张建忠1,傅小波1,2,3,廖祖华2,3+   

  1. 1. 无锡职业技术学院 基础部,江苏 无锡 214121
    2. 江南大学 理学院,江苏 无锡 214122
    3. 江南大学 教育部物联网技术应用工程研究中心,江苏 无锡 214122

Abstract: A detailed investigation on the (∈,∈∨q(λ,μ))-fuzzy ideal of N(2,2,0) algebra is carried out from the following aspects. Firstly, this paper introduces the concepts of generalized fuzzy ideal and pointwise (∈,∈∨q(λ,μ))-fuzzy ideal,and discusses the relationship between them. Secondly, this paper presents some equivalent descriptions of the (∈,∈∨q(λ,μ))-fuzzy ideal, and studies the related properties. Thirdly, this paper discusses some basic properties of homomorphic image and homomorphic preimage of the(∈,∈∨q(λ,μ))-fuzzy ideal. Finally, the direct product of the (∈,∈∨q(λ,μ))-fuzzy ideal is also studied.

Key words: N(2,2,0)algebra, generalized fuzzy ideal; (∈,∈∨q(λ,μ))-fuzzy ideal, homomorphism, direct product

摘要: N(2,2,0)代数(∈,∈∨q(λ,μ))-模糊理想进行了详细的研究。给出了N(2,2,0)代数广义模糊理想和点态化(∈,∈∨q(λ,μ))-模糊理想的概念,讨论了两者之间的等价关系。给出了(∈,∈∨q(λ,μ))-模糊理想的一些等价刻画,并研究了其相关性质。讨论了(∈,∈∨q(λ,μ))-模糊理想的同态像与同态原像的关系。最后研究了(∈,∈∨q(λ,μ))-模糊理想的直积。

关键词: N(2, 2, 0)代数, 广义模糊理想,  , (&isin, &isin, &or, q(&lambda, &mu, ))-模糊理想, 同态, 直积