属性拓扑与属性偏序双向转化

Bidirectional transformation between attribute topology and attribute partial order

属性拓扑和属性偏序是近年来新提出的两种形式背景表示方法。其中,属性拓扑基于属性耦合关系实现形式背景的简洁可视化表示,并发展出多种形式概念计算方法。属性偏序则以偏序关系为基础表示形式背景。针对两种新方法在形式概念分析领域中的互补关系,本文从集合论的角度论述属性拓扑与属性偏序双向转化的数学基础,描述不同二元关系下二者的转化原理与方法,并在此基础上提出属性拓扑和属性偏序双向转化算法,实现二者等价可逆转化,为形式背景提供统一的表示基础。

Attribute topology and attribute partial order are put forw ard to represent formal context recently. Based on the coupling betw een attributes,the simple visual representation of the formal context is achieved by attribute topology and the various forms of calculation methods are developed. Additionally,attribute partial order is based on partial order to represent formal concept. For the complementary relationships betw een the tw o new methods in the field of formal concept analysis,the mathematical basis of the bidirectional transformation of attribute topology and attribute partial order are discussed from the perspective of set theory on this paper,w here the transformation principles and methods of them are described in different binary relations. And the algorithm of the bidirectional transformation of attribute topology and attribute partial order based on the above is put forw ard,equivalent reversible conversion of them is achieved,and an unified representation basis for formal context is provided.