两类概念格的依赖空间理论

Dependence Space Based on Two Types of Concept Lattices

对象定向概念格和属性定向概念格是经典概念格的两种推广模型。首先,利用对象幂集上的一对对偶近似算子分别定义了对象定向概念格和属性定向概念格上的同余关系。其次,分别基于两类同余关系构造了一个内部算子和一个闭包算子,并研究了内部算子与对象定向概念格的关系以及闭包算子与属性定向概念格的关系。最后将对象(属性)定向概念格之间的关系转化为相应的同余关系之间的关系。

Object oriented concept lattice and attribute oriented concept lattice are two types of generalized models of classical concept lattice. Firstly, two congruence relations were defined respectively on object power sets of object orien- ted concept lattice and attribute oriented concept lattice using a pair of dual approximation operators. Secondly, an inner operator and a closure operator were constructed based on two kinds of congruence relations. Then relationship between the inner operator and object oriented concept lattice was studied as well as relationship between the closure ope- rator and attribute oriented concept lattice. Finally, relationships between two object oriented concept lattices were transformed into relationships between the corresponding congruence relations.