信息系统同态的性质及上下近似的不变性

作为研究信息系统之间关系的一种有力工具,信息系统同态的概念首先由J.W.Grzyrnala-Busse引入。本文研究了信息系统同态的一些性质,揭示了构成信息系统同态的对象映射、属性映射与值域映射之间的相互依赖性。由给定的论域上的划分,导出了一个新的信息系统同态,该同态对论域的划分与给定划分相同。同时,讨论了信息系统在同态的意义下,上近似与下近似的不变性,为粗糙集理论的进一步研究奠定了理论基础。

Some Characters of Information System Homomorphism and Invariance of Upper and Lower Approximations

The notion of an information system homomorphism,as a powerful tool to study the relation between two information systems,is introduced by J.W.Grzymala-Busse.This paper discusses some characters of information sys- tem homomorphism,reveals the interdependence of three mappings,namely,object mapping,attribute mapping and value domain mapping.Besides,given a partition on universe,a new information system homomorphism can been de- rived,which defines a partition on universe identical with the partition given.At the same time,some invariant charac- ters of upper approximation and lower approximation under information system homomorphism are presented,which establish the theoretical foundation for further studies of rough set theory.