面向属性(对象)概念格基于直观图的保并(交)约简

MIE-preserving reduction and JIE-preserving reduction of property(object)-oriented concept lattices based on the pictorial diagram

属性约简是形式概念分析中的一个重要问题,文中主要研究面向属性概念格和面向对象概念格的保持并(交)不可约元外延不变的约简。给出面向属性概念格和面向对象概念格的保并约简和保交约简的定义;研究了这两个格的保并约简和保交约简之间的关系;利用形式背景直观图,给出获取这两种格的保并约简和保交约简的理论与方法。

Attribute reduction is an important issue in formal concept analysis. This paper mainly studies MIE （meet irreducible element）-preserving reduction and JIE （join irreducible element）-preserving reduction of property-oriented and object-oriented concept lattices. Firstly, the definitions of MIE-preserving reduction and JIE-preserving reduction of property-oriented and object-oriented concept lattices are given. Then, the rela- tionship between MIE （JIE）-preserving reduction in property-oriented and its counterpart in object-oriented concept lattices is presented. Finally, pictorial diagram is used to give the theory and method of finding the MIE-preserving reduction and JIE-preserving reduction.