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One of the key issues in the theory of concept lattices is to extract the useful rules from the decision formal context. The maximal rules implicate the others, thus people are interested in them. This paper proposes two new kinds of attribute reduction in the decision formal context based on maximal rules. The reducts preserve all the condition extensions and the decision extensions related to the original maximal rules. The internal relationship between the original maximal rules and the maximal rules in the reduced decision formal context is derived. The reducts can make the maximal rules more concise and accurate. The mathematical property of the proposed attribute reduction is investigated and we construct the discernibility matrix and function to compute all the reducts. Finally, all the attributes are classified into three types based on the maximal rules. The characteristics of these types of attributes are also analyzed.

Attribute reduction based on maximal rules in decision formal context