Attribute Reduction of Object Granules of Concept Lattice Based on Three-Way Decision

Formal concept analysis is a key tool in data analysis and knowledge representation and a specific method for granular computing. Object granules constitute the basic granular knowledge in a concept lattice. Three-way decision is a reasonable approach to extracting decision rules. This study employs the principle of three-way decision to divide all the object granules of a formal context into three parts: positive, negative and boundary regions, then two groups of certainty decision rules are extracted from the positive region and the negative region, and one group of possibility decision rules is induced from the boundary region. The notion of attribute reduction keeping the performance of the decision rules unchanged are proposed. An approach for computing attribute reducts is put forward by utilizing the discernibility matrix and discernibility function. Some examples are taken to explain or show the relevant conclusions and prove the feasibility of the reduction method.