真蕴涵格与优蕴涵格  

Proper Implication Lattices and Well Implication Lattices

作　　者：刘汇洋[1] 张小红[1] 

机构地区：[1]宁波大学数学系,浙江宁波315211

出　　处：《模糊系统与数学》2010年第6期17-26,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(60775038);宁波大学王宽诚幸福基金资助项目

摘　　要：研究蕴涵格的性质及其结构。借助数学软件给出8阶及以下蕴涵格的完全分类,说明了真蕴涵格与优蕴涵格的存在性,并纠正了多个文献中关于蕴涵格的一些错误结论。同时,引入局部有限蕴涵格和次结合蕴涵格的概念,证明了局部有限蕴涵格是优蕴涵格。The properties and structure of implication lattices are investigated. The classification of implication lattices with 8（and lower） orders is solved by Mathematica programs,and some mistakes of references are pointed out.Moreover,the notions of locally finite implication lattice and sub-associative implication lattice are introduced,some properties of them are discussed,and the following result is proved： every locally finite implication lattice is well implication lattice.

关 键 词：蕴涵格 真蕴涵格 优蕴涵格 局部有限蕴涵格 次结合蕴涵格 

分 类 号：O141[理学—数学]