ABSTRACT Homomorphisms between information systems as a kind of tools to study communication between information systems are based on data compression, i.e. a complex massive information system is compressed into a relatively small-scale information system by means of homomorphisms under the premise that some of the same data structures are maintained. This paper is devoted to obtaining some invariant and inverse invariant characters of information systems under homomorphisms based on data compression. Saturation reductions of an information system is first proposed. Then, relationships between reductions and saturation reductions of the same information system are given. Next, information structures in information systems are further investigated. Finally, it is proved that coordinate sets, necessary attributes, necessary s-attributes, saturated coordinate sets, saturation reductions, some dependence and independence between information structures in an information system are both invariant and inverse invariant under homomorphisms based on data compression, in other words, some of the same data structures of an information system are obtained. Moreover, an example is used to illustrate that information granulation, rough entropy, information entropy and information amount are neither invariant nor inverse invariant under homomorphisms based on data compression.

中文翻译：

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基于数据压缩的同态下信息系统的若干不变性和逆不变性特征

摘要 信息系统间同态作为研究信息系统间通信的一种工具是基于数据压缩的，即将一个复杂的海量信息系统通过同态的方式压缩成一个规模相对较小的信息系统。数据结构得到维护。本文致力于在数据压缩的基础上获得同态下信息系统的一些不变性和逆不变性。信息系统的饱和度降低首先被提出。然后，给出了同一信息系统的减少和饱和减少之间的关系。接下来，进一步研究信息系统中的信息结构。最后证明坐标集、必要属性、必要s属性、在基于数据压缩的同态下，信息系统中的饱和坐标集、饱和度降低、信息结构之间的一些依赖和独立性既是不变的又是逆不变的，换句话说，获得了信息系统的一些相同的数据结构。此外，还通过一个例子来说明在基于数据压缩的同态下，信息粒度、粗熵、信息熵和信息量既不是不变的，也不是逆不变的。