Using the Choquet Integral for the Determination of the Anxiety Degree

This paper introduces a mathematical model describing how the EEG type waves are processed in order to characterize the level of anxiety. The electroencephalogram (EEG) is a recording of the electrical activity of the brain. The main frequencies of the human EEG waves are: Delta, Theta, Alpha (Low Alpha and High Alpha), Beta (Low Beta and High Beta), Gamma. Psychologists' studies show that there is an interactive relationship between anxiety and two factors in the Big Five theory, namely, extraversion and neuroticism. The specialists in psychology state that the anxiety is characterized by LowAlpha, HighAlpha, LowBeta and HighBeta waves. In this regard, we developed a mathematical model through which EEG waves are processed in order to determine the level of anxiety. Our main idea is to use the Choquet integral with respect to a suitable monotone measure in order to characterize the level of anxiety. This measure was obtained using the measurements of the values of EEG waves made on 70 subjects and the corresponding levels of anxiety (established by psychologists) of these subjects. In order to verify our mathematical model (aggregation tool) we used it to determine the level of anxiety of 10 other subjects, comparing our results with the results provided by psychologists (the comparison validated our results).