Matrix-Type Attribute Reduction for Inconsistent Formal Decision Contexts

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.

Keywords

• attribute reduction
• heuristic algorithm
• inconsistent formal decision contexts
• similarity