不完备知识下的形式概念表示与计算

Representation and Computing of Formal Concepts under Incomplete Knowledge

从集合的角度来说,知识就是数据集合在某种关系下的划分。如果这个数据集的某些属性值是未知的或丢失了,那么知识就是不完备(incomplete)的。传统形式概念分析是源于完备数据集的(完备知识)。在不完备知识下的概念分析一般说来比完备知识更困难。本文提出了一个新的不完备知识下形式概念表示与计算的方法,这种方法是基于泛化粗糙集理论的,其目的是扩展形式概念分析研究的领域。文中研究了一个基于自反相似关系的粗糙集模型,讨论了基于这种模型的形式概念分析方法。一个实例表明了这种方法的可行性。

From the point of view of the set, knowledge is a partition of data set about some relations. It is incomplete if some attribute values are unknown or missing in the data set. The classical formal concept analysis derives from complete data set （complete knowledge）. Concept analysis under incomplete knowledge is usually more difficult. This paper presents new approaches to represent and compute formal concepts under incomplete knowledge. It is based on generalized rough set theory, and aims to extend formal concept analysis to the condition of incomplete knowledge. A rough set model on reflexive similarity relation is discussed. The approaches of formal concept analysis, build on the model, are proposed. Finally an example is given to show the feasibility of the proposed method.