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Intervals are a popular way to represent the uncertainty related to data, inwhich we express the vagueness of each observation as the width of theinterval. However, when using intervals for this purpose, we need to use theappropriate set of mathematical tools to work with. This can be problematic dueto the scarcity and complexity of interval-valued functions in comparison withthe numerical ones. In this work, we propose to extend a generalization of theSugeno integral to work with interval-valued data. Then, we use this integralto aggregate interval-valued data in two different settings: first, we studythe use of intervals in a brain-computer interface; secondly, we study how toconstruct interval-valued relationships in a social network, and how toaggregate their information. Our results show that interval-valued data caneffectively model some of the uncertainty and coalitions of the data in bothcases. For the case of brain-computer interface, we found that our resultssurpassed the results of other interval-valued functions.

A Generalization of the Sugeno integral to aggregate Interval-valued data: an application to Brain Computer Interface and Social Network Analysis