粗糙集代数与蕴涵格

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。

Rough Set Algebra and Implication Lattice

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 d by the pairs becomes an implication lattice. The relation between the regular double Stone algebra and the rough implication lattice is studied. The r esults can lay a foundation for rough logic and rough reasoning.