Journal of Frontiers of Computer Science and Technology ›› 2016, Vol. 10 ›› Issue (8): 1191-1200.DOI: 10.3778/j.issn.1673-9418.1507061

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(ˉ∈,ˉ∈ ∨ˉq(λ,μ)) -Fuzzy Ideals of Incline Algebras

LU Teng1, LIAO Zuhua1,2+, LIAO Cuicui1,2, YUAN Wangui1,2   

  1. 1. School of Science, Jiangnan University, Wuxi, Jiangsu 214122, China
    2. Institute of Intelligence System & Network Computing, Jiangnan University, Wuxi, Jiangsu 214122, China
  • Online:2016-08-01 Published:2016-08-09

坡代数的(ˉ∈,ˉ∈ ∨ˉq(λ,μ)) -模糊理想

路  腾1,廖祖华1,2+,廖翠萃1,2,袁玩贵1,2   

  1. 1. 江南大学 理学院,江苏 无锡 214122
    2. 江南大学 智能系统与网络计算研究所,江苏 无锡 214122

Abstract: Firstly, this paper introduces the concept of (ˉ∈,ˉ∈ ∨ˉq(λ,μ))-fuzzy ideal of incline algebra and discusses some equivalent characterizations. Then this paper proves that the union and the anti-direct product of (ˉ∈,ˉ∈ ∨ˉq(λ,μ))- fuzzy ideals of incline algebras are still (ˉ∈,ˉ∈ ∨ˉq(λ,μ))-fuzzy ideals of incline algebras, and obtains some relative properties of its isomorphic image and homomorphic preimage based on the anti-extension principle. Finally, this paper discusses some basic properties of (ˉ∈,ˉ∈ ∨ˉq(λ,μ))-fuzzy ideals of incline algebras through the chain condition of filters of incline algebras. The new concept of (ˉ∈,ˉ∈ ∨ˉq(λ,μ))-fuzzy ideal of incline algebras expands the study of incline algebraic theory.The properties of chain condition of filters of incline algebras can also be applied to other algebraic structures, these new results enrich the soft algebra theory.

Key words: (ˉ∈,ˉ&isin, ∨ˉq(λ,μ))-fuzzy ideals, filters, chain condition, homomorphic preimage, isomorphic image

摘要: 给出了坡的(ˉ∈,ˉ∈ ∨ˉq(λ,μ))-模糊理想的概念,研究了坡的(ˉ∈,ˉ∈ ∨ˉq(λ,μ))-模糊理想的等价刻画,得到了坡的(ˉ∈,ˉ∈ ∨ˉq(λ,μ))-模糊理想在并运算与反直积运算下封闭的结论;利用反扩张原理获得了坡的(ˉ∈,ˉ∈ ∨ˉq(λ,μ))-模糊理想的同态原像与同构像的性质;最后,引入了坡的滤子的链式条件,并讨论了它的一些基本性质。坡的(ˉ∈,ˉ∈ ∨ˉq(λ,μ))-模糊理想新概念的提出扩展了坡代数理论的研究,引入的坡的滤子的链式条件的性质也可应用于其他代数结构,丰富了软代数理论研究。

关键词: (ˉ∈,ˉ&isin, ∨ˉq(λ,μ))-模糊理想;滤子;链式条件;同态原像;同构像