格蕴涵代数的直觉模糊LI-理想

On Intuitionistic Fuzzy LI-ideals in Lattice Implication Algebras

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

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.