F格上的逼近算子

The Approximation Operator on F-Lattice

粗集理论是波兰学者Pawlak提出的知识表示新理论.Pawlak代数是粗集理论中粗集系统的抽象,其公理系统包含了知识粗表示所必须的全部性质.本文深入研究了F格上的逼近算子,建立了F格上弱逼近算子之间的某些代数运算,从而从理论上建立了各种知识粗表示之间的联系.我们还定义了逼近算子的闭包,进而用逼近算子导出拓扑,为信息系统的近似提供必要的数学基础.最后,作为特例,我们研究了粗集理论中由相似关系导出逼近算子的某些性质.

In this paper, Pawlakean algebra is a abstract modei of the rough set system. We have discussed the lattice of a weak approximation operator introduced by the order relation on an operator space. By defining the closure operator of an approximation operator, the approximation operator is connected with topology on F-lattice. This connection provides mathematical basis for approximate representation of uncertain information systems. At last, the approximation operator deduced by similar relation is discussed in rough set theory.