Minimal Sub-bases For Data Topological Spaces

This dissertation investigates minimal sub-bases and a minimal family of sub-bases in data topological spaces.The main results include minimal sub-bases and its properties,an approach to derive a minimal family of sub-bases,and the relationship between minimal families of subbases and reducts of covering information systems.These results are chapter two and three.Chapter 2 discusses minimal bases and minimal sub-bases for topological spaces.Firstly,the necessary and sufficient condition about the existence of minimal base for Alexandroff spaces is extended to general topological spaces.Secondly,the definition of minimal sub-base is proposed and its properties are concerned.Finally,the relationship between minimal bases and minimal sub-bases is considered.Chapter 3 studies a minimal family of sub-bases.Firstly,the concept of a minimal family of sub-bases is introduced and its properties are researched.Secondly,the relationship between minimal families of sub-bases and reducts of covering information systems is analyzed.Finally,an algorithm to derive a minimal family of sub-bases is provided,and several numerical experiments on UCI data sets are conducted to illustrate the effectiveness of the proposed algorithm.