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In this work we introduce the notion of preaggregation function. Such a function satisfies the same boundary conditions as an aggregation function, but, instead of requiring monotonicity, only monotonicity along some fixed direction (directional monotonicity) is required. We present some examples of such functions. We propose three different methods to build pre-aggregation functions. We experimentally show that in fuzzy rule-based classification systems, when we use one of these methods, namely, the one based on the use of the Choquet integral replacing the product by other aggregation functions, if we consider the minimum or the Hamacher product t-norms for such construction, we improve the results obtained when applying the fuzzy reasoning methods obtained using two classical averaging operators like the maximum and the Choquet integral.

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Brain-computer interface technologies, such as steady-state visually evoked potential, P300, and motor imagery are methods of communication between the human brain and the external devices. Motor imagery-based brain-computer interfaces are popular because they avoid unnecessary external stimulus.Although feature extraction methods have been illustrated in several machine intelligent systems in motor imagery-based brain-computer interface studies, the performance remains unsatisfactory. There is increasing interest in the use of the fuzzy integrals, the Choquet and Sugeno integrals, that are appropriate for use in applications in which fusion of data must consider possible data interactions. To enhance the classification accuracy of brain-computer interfaces, we adopted fuzzy integrals, after employing the classification method of traditional brain-computer interfaces, to consider possible links between the data. Subsequently, we proposed a novel classification framework called the multimodal fuzzy fusion-based brain-computer interface system. Ten volunteers performed a motor imagery-based brain-computer interface experiment, and we acquired electroencephalography signals simultaneously.