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
格蕴涵代数的直觉模糊LI-理想
On Intuitionistic Fuzzy LI-ideals in Lattice Implication Algebras
投稿时间:2014-09-02  最后修改时间:2014-12-22
DOI:10.3770/j.issn:2095-2651.2015.04.001
中文关键词:  格值逻辑  格蕴涵代数  直觉模糊LI-理想.
英文关键词:lattice-valued logic  lattice implication algebra  intuitionistic fuzzy \emph{LI}-ideal
基金项目:国家自然科学基金 (Grant No.60774073).
作者单位
刘春辉 赤峰学院数学与统计学院, 内蒙古 赤峰 024001 
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中文摘要:
      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.
英文摘要:
      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.
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