Abstract:

Attribute reduction is a powerful tool about knowledge representation and data analysis in formal concept analysis. There are many approaches of attribute reduction for inconsistent formal decision contexts. In this paper, the attribute reduction of inconsistent formal decision contexts is studied based on Boolean matrix, and a new description of attribute reduction is developed. First, the generalized matrix consistent set based on Boolean matrix operations is defined, and the measurement of similarity between attributes is proposed. Subsequently, conditional attributes are divided into core attributes and non-core attributes depending on the importance of attributes in the process of attribute reduction. The equivalent judgment whether an attribute is a core attribute is proposed, and a discriminated method to attribute reduction is provided. Finally, a heuristic attribute-reduction algorithm is developed in terms of the above framework and an example is conducted to illustrate that the algorithm is reasonable and feasible. Through attribute reduction, the computation of concept lattice in this form is simpler. The above results in this paper provide a research basis for the further study in application and theoretical basis for the study of matrix approach in formal concept analysis.

Key words: attribute reduction, heuristic algorithm, inconsistent formal decision contexts, similarity

摘要：

形式概念分析的属性约简是知识表达和数据处理的一种有力的工具。对于不协调决策形式背景，已有多种属性约简的方法。从布尔矩阵运算的角度研究不协调决策形式背景的属性约简问题，提出属性约简的新的刻画。首先，借助矩阵的运算给出广义矩阵协调集的定义，并研究属性之间相似性的度量。接着，针对在属性约简过程中起不同作用的属性，将条件属性区分为核心属性和非核心属性，提出一个属性是否是核心属性的充要判断条件，以及得出属性约简的判别方法。最后，在此框架上设计出不协调决策形式背景属性约简的一种启发式算法，通过例题说明此算法的可行性和合理性。通过属性约简，该形式背景下的概念格计算更为简便。上述结果有助于进一步的应用及为研究形式概念分析的矩阵方法提供理论基础。

关键词: 属性约简, 启发式算法, 不协调决策形式背景, 相似度