In this work we study the use of moderate deviation functions to measure similarity and dissimilarity among a set of given interval-valued data. To do so, we introduce the notion of interval-valued moderate deviation function and we study in particular those interval-valued moderate deviation functions which preserve the width of the input intervals. Then, we study how to apply these functions to construct interval-valued aggregation functions. We have applied them in the decision making phase of two Motor-Imagery Brain Computer Interface frameworks, obtaining better results than those obtained using other numerical and intervalar aggregations.