单调概念格性质研究  

A Research on Monotone Concept Lattices

作　　者：杨田[1] 伍秀华[1] 金检华[2] 

机构地区：[1]中南林业科技大学理学院,湖南长沙410004 [2]湖南大学数学与计量经济学院,湖南长沙410082

出　　处：《模糊系统与数学》2012年第4期185-190,共6页Fuzzy Systems and Mathematics

基　　金：湖南省科技厅科技计划项目(2011FJ3152);湖南省研究生科技创新项目(CX2011B158)

摘　　要：概念格是知识表示和数据分析的重要工具,单调概念格是概念格的推广。本文就Deogun等提出的单调概念格进行了两方面的研究:一,指出Deogun等提出的单调概念格性质的错误并加以修正;二,证明单调概念格就是闭格,从而找到用拓扑闭包算子和拓扑交结构来表示单调概念格的两种格表示方法,并建立起单调概念格与有上界的拓扑交结构的范畴等价。本文所建立的单调概念格的拓扑表示方法将方便我们进一步研究单调概念格的构造算法、约简算法和实际应用,具有理论和实际的双重意义。Concept lattice is a important method for data analysis and knowledge representation, monotone concept lattice is an extention of classical concept lattice.This paper study the monotone concept lattice proposed by Deogun from three aspects：（1）Point out the errors on propositions of monotone concept lattice in Deogun＇s paper,and correct them.（2）Prove that a monotone concept lattice is a closed lattice.As a result, find two ways to represent monotone concept lattices by topological intersection structures and topological closure operators.Moreover,construct categorical equivalence between monotone concept lattices and topological intersection structures.The propositions suggest new methods of construction algorithms,reduction algorithms and applications of monotone concept lattices. The research provides theoretical and practical significance.

关 键 词：概念格 闭格 格表示 同构 范畴等价 

分 类 号：O189[理学—数学]