Interval-Valued Aggregation Functions Based on Moderate Deviations Applied to Motor-Imagery-Based Brain–Computer Interface

In this article, we develop moderate deviation functions to measure similarity and dissimilarity among a set of given interval-valued data to construct interval-valued aggregation functions, and we apply these functions in two motor-imagery brain–computer interface (MI-BCI) systems to classify electroencephalography signals. To do so, we introduce the notion of interval-valued moderate deviation function and, in particular, we study those interval-valued moderate deviation functions, which preserve the width of the input intervals. In order to apply them in an MI-BCI system, we first use fuzzy implication operators to measure the uncertainty linked to the output of each classifier in the ensemble of the system, and then we perform the decision making phase using the new interval-valued aggregation functions. We have tested the goodness of our proposal in two MI-BCI frameworks, obtaining better results than those obtained using other numerical aggregation and interval-valued ordered weighted averaging operators, and obtaining competitive results versus some nonaggregation-based frameworks.