商空间理论与粗糙集的比较

To Compare the Theory of Quotient Space with Rough Set

文中以比较的方式讨论了粗糙集理论和商空间理论之间的关系,通过对两理论基本算法及复杂度和理论扩展的分析,得出商空间理论与目前流行的"粗糙集"理论的共同之处在于:都是利用等价类来描述"粒度",都是用"粒度"来描述概念。但两者讨论的着重点有所不同,商空间理论的着重点是研究不同粒度世界之间的互相转换、互相依存的关系,是描述空间关系学说的理论;而目前的粒度计算(如粗糙集理论等)主要是研究粒度的表示、刻画和粒度与概念之间的依存关系。更主要的不同在于:商空间理论是在论域元素之间存在有拓扑关系的情况下进行研究的,即论域是一个拓扑空间,而现在的粗糙集理论其论域只是简单的点集,元素之间没有拓扑关系,因此商空间理论不仅可用于数据挖掘、知识发现等方面的应用,而且对路程规划、空间状态分布等约束问题同样适用。

The relationship between rough set and quotient space is discussed by comparing in the paper.After analyzing basic algorithms and complexity and expansibility in theory about rough set and quotient space,think that the same point of them is to represent granule by using equivalence relation and to depict concept by using granule.But the emphasis of both discussions is difference.The theory of quotient space researches transformed and depended relations between different granules mainly.It is the theory to represent space relationship.For granular computing today such as rough set,it studies to represent and depict granule and relation between granule and concept primarily.The greatest difference is that there is topological relation among domain elements in the theory of quotient space,i.e.the domain is a topological space.Whereas the domain of rough set is only simple point set,there is no topological relation among elements.So the theory of quotient space applies to not only data mining and knowledge discovery,but also restriction problem such as route layout and space state distributing etc.