Attribute Reduction Method For Concept Lattices Based On Boolean Matrices

The concept lattice is a mathematical method of data analyse and knowledge processing,which is based on hierarchy relation among concepts. With the increasing amount of data,how to use these effective methods to find the useful information and make it invalid isnecessary. So the attribute reduction of concept lattices plays an important role. Then ZhangWen-xiu raised attribute reduction in concept lattices based on discernable matrix. But thesolution of all formal concepts is a precondition of solving discernable matrix in conceptlattice. And the solution of all formal concepts is another question in the concept lattice. Thenwe propose a new method of attribute reduction by using Boolean matrix. The advantage ofthis new method is that it does not need to compute all the formal concepts to obtain theattribute reducts of a concept lattice.Firstly, we use Boolean matrices to character formal context, a subset of the object or asubset of the properties is characterized by eigenvectors. We define object relation matrix,attribute relation matrix, object inclusion relation matrix, attribute inclusion relation matrix,object equivalent matrix, and attribute equivalent matrix. Based on the Boolean matrixoperation method, we proposed the intension and extension of a set of the formal context.Secondly, this paper also study judgment of consistent sets, attribute determination andattribute reductions of formal context. We construct consistent judge matrix in formal context.Compared with the relation matrix of formal context,we can judge a set whether to be aconsistent set. Then define the core judge matrix. Therefore, we obtain a way that determiningattribute characteristics base on core judge matrix.Then we proposed the method ofconstruting reduction set.Finally, this paper study judgment of consistent sets of decision formal context, defineconsistent judge matrix in decision formal context. Compared with consistent judge matrix indecision formal context, we can judge a set whether to be a consistent set.