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格蕴涵代数的直觉模糊LI-理想
引用本文:刘春辉.格蕴涵代数的直觉模糊LI-理想[J].数学研究及应用,2015,35(4):355-367.
作者姓名:刘春辉
作者单位:赤峰学院数学与统计学院, 内蒙古 赤峰 024001
基金项目:国家自然科学基金 (Grant No.60774073).
摘    要:本文深入研究了格蕴涵代数的直觉模糊\textit{LI}-理想理论.给出了直觉模糊\textit{LI}-理想的若干新的性质和等价刻画. 建立了由一个直觉模糊集生成的直觉模糊\textit{LI}-理想的表示定理.证明了一个格蕴涵代数的全体之集模糊\textit{LI}-理想之集在直觉模糊包含序下构成一个完备的分配格.

关 键 词:格值逻辑    格蕴涵代数    直觉模糊LI-理想.
收稿时间:9/2/2014 12:00:00 AM
修稿时间:2014/12/22 0:00:00

On Intuitionistic Fuzzy LI-ideals in Lattice Implication Algebras
Chunhui LIU.On Intuitionistic Fuzzy LI-ideals in Lattice Implication Algebras[J].Journal of Mathematical Research with Applications,2015,35(4):355-367.
Authors:Chunhui LIU
Institution:Department of Mathematics and Statistics, Chifeng University, Inner Mongolia 024001, P. R. China
Abstract:In the present paper, the intuitionistic fuzzy LI-ideal theory in lattice implication algebras is further studied. Some new properties and equivalent characterizations of intuitionistic fuzzy LI-ideals are given. Representation theorem of intuitionistic fuzzy LI-ideal which is generated by an intuitionistic fuzzy set is established. It is proved that the set consisting of all intuitionistic fuzzy LI-ideals in a lattice implication algebra, under the inclusion order, forms a complete distributive lattice.
Keywords:lattice-valued logic  lattice implication algebra  intuitionistic fuzzy \emph{LI}-ideal
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