Attribute reduction based on interval-valued formal contexts

The interval value is frequently used when describing the problems of uncertainty. The attribute reduction of concept lattice refers to the minimal set of attributes that consistently maintain a certain characteristic sought under the condition that the object set is maintained unchanged. Through the study of the interval value and the nature of Galois connection, this paper is to provide a pair of Galois connection in the context of an interval form to generate an interval concept. Moreover, an interval concept lattice whose form and context are identical with the original interval value is constructed. And then this paper is to study the theories and methods of the reduction of the attribute value vector of the interval concept lattice.