粗糙集代数与蕴涵格  

Rough Set Algebra and Implication Lattice

作　　者：陈世联[1] 

机构地区：[1]淮阴工学院计算科学系,江苏淮安223002

出　　处：《计算机工程与科学》2008年第5期115-117,共3页Computer Engineering & Science

摘　　要：在粗糙集的代数刻画方面,一个重要方法是在偶序对〈R（X）,R（X）〉构成的集合中通过定义基本运算寻找刻画偶序对所成集合的代数结构。其中,最有影响的代数结构是正则双Stone代数和Nelson代数。本文从偶序对〈T（X）,R（X）〉构成的集合入手,通过定义蕴涵运算证明了偶序对〈R（X）,R（X）〉所成集合构成蕴涵格,讨论了粗蕴涵格与正则双Stone代数的关系。本文的讨论可为粗糙逻辑和粗糙推理奠定基础。In the research of the rough set theory by algebraic approaches, an important method is to define some basic operators in the set of the pairs 〈R（X）,R（X） 〉 , and find the algebraic structure constructed by the pairs. The most famous algebraic structures are the regular double Stone algebra and the Nelson algebra. The paper starts from the set of pairs 〈R（X）, -R（X）〉 , by defining an implication operator, proves that this rough set formed by the pairs becomes an implication lattice. The relation between the regular double Stone algebra and the rough implication lattice is studied. The results can lay a foundation for rough logic and rough reasoning.

关 键 词：粗糙集 粗糙集代数 蕴涵格 正则双Stone代数 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]