格蕴涵代数的素模糊LI-理想及其谱空间  

Prime fuzzy LI-ideals and its spectrum space of lattice implication algebras

作　　者：刘春辉[1] 

机构地区：[1]赤峰学院数学与统计学院,内蒙古赤峰024001

出　　处：《高校应用数学学报（A辑）》2014年第1期115-126,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10371106;60774073)

摘　　要：运用模糊集及拓扑学的方法和原理对格蕴涵代数的LI-理想概念作进一步研究.首先,在格蕴涵代数中引入素模糊LI-理想的概念并讨论其性质特征及其与LI-理想的关系,建立了格蕴涵代数的素模糊LI-理想定理.其次,在格蕴涵代数L的全体素模糊LI-理想构成的集合PFLI(L)上构造了一个拓扑T,从而得拓扑空间(PFLI(L),T),称之为L的素模糊LI-理想谱空间,记为P F-Spec(L).考察了P FSpec(L)的若干拓扑性质.最后,在格蕴涵代数L的全体素LI-理想之集PLI(L)上定义了LI-拓扑TLI,证明了在一个格H蕴涵代数中拓扑空间(PLI(L),TLI)同胚于P FSpec(L)的一个Hausdor?子空间的结论.The aim of this paper is to further study the concept of LI-ideals in lattice implication algebras by using the method and principle of fuzzy sets and topology. Firstly, the notion prime fuzzy LI-ideals in lattice implication algebras is introduced and their properties are studied. And the prime fuzzy LI-ideals theorem of lattice implication algebras is established. Secondly, a topology T is constructed on the set of all prime fuzzy LI-ideals P FLI （L） in an lattice implication algebra L, then a topological space （PFLI（L）, T ） is obtaind, be called prime fuzzy LI-ideals spectrum space of L, and denoted by P F-Spec（L）. Some topological properties of P F-Spec（L） are discussed. Finally, the LI-topology is defined on the set of all prime LI-ideals PLI （L） of L. It is proved that topological space （PLI （L）, TLI ） homeomorphic with an Hausdorff subspace of P F-Spec（L） in a lattice H implication algebra.

关 键 词：模糊逻辑 格蕴涵代数 (素)LI-理想 素模糊LI-理想 谱空间 

分 类 号：O159[理学—数学]