对象定向概念格的决策约简

摘要

This paper presents a notion and a method of attribute reduction for object oriented concept lattice of a decision formal context. An equivalent relation defined on the object power set is first introduced into the object oriented concept, and then relative properties of the relation are discussed. Based on the equivalent relation a notion of consistency is defined for a decision formal context. Furthermore attribute reduction for a consistent decision formal context is presented which can preserve all equivalent classes decided by the original attribute set and also preserve the original lattice structures of all extents. Finally a method of discernible matrix is proposed to obtain attribute reducts.%研究了基于对象定向概念格的决策形式背景的属性约简的定义和方法。在对象幂集上引入一个等价关系，并介绍了相关性质。提出了决策形式背景的协调性的定义，进而利用等价关系给出了协调决策形式背景的属性约简定义。该定义下的属性约简集能保持由原属性集确定的所有等价类不变的最小属性子集，同时它也能保持所有对象定向概念的外延不变。利用辨识矩阵提出了一种用于计算所有属性约简集的方法。