On Intuitionistic Fuzzy LI-ideals in Lattice Implication Algebras

DOI：10.3770/j.issn:2095-2651.2015.04.001

 作者 单位 刘春辉 赤峰学院数学与统计学院, 内蒙古 赤峰 024001

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.

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.