Distributive Reduction of Attributes in Concept Lattice

Attribute reduction is one of the key problems in formal concept analysis. A few approaches have been proposed but they are only applicable to formal context in a non-distributed environment. With the wide application of distributed data storage and processing, it is necessary to develop a method to adapt to this environment. To address this problem, the characterizations of different kinds of attributes are provided from the point of view of global context and local context. The notion of super set and consistent set are introduced to determine whether an attribute is reducible in a global context. The determinant theorem of attribute reductions is derived based on core attributes and dispensable attributes. Based on these results, two algorithms are designed to compute attribute reductions of context in a distributed environment. The first algorithm, DRCL, determines attribute reductions of global context. The local reductions can be computed by using the existing approaches. The second algorithm, ADSCL, determines the super sets and all minimal consistent sets for the attributes given by a context. This information is required by the first algorithm. Theory analysis and experimental results show the feasibility and effectiveness of the two algorithms.