Formal concept analysis of multi-scale formal context

The case that attributes have a single value is considered in the classical formal concept. However, real-life data involve multi-level attribute values, which means that attributes have different values on different scales. In order to deal with multi-level attributes, we introduce the concept of multi-scale formal context in this paper. In this context, with the change of scale, objects owned by each attribute change monotonously. Thus, under the multi-scale formal context, the change of formal concept is discussed. Moreover, this paper defines the consistent multi-scale formal decision context and discusses the optimal scale selection problem of the consistent multi-scale decision context.