Using the Choquet Integral for the Determination of the Anxiety Degree

Abstract

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).

Convergence Theorems in Interval-Valued Riemann–Lebesgue Integrability

“…The theory of non-additive set functions and nonlinear integrals has become an important tool in many domains such as: potential theory, subjective evaluation, optimization, economics, decision making, data mining, artificial intelligence, accident rates estimations (e.g. [20,21,38,44,53,56,60,63,75,[79][80][81]84]). In the literature several methods of integration for (multi)functions based on extensions of the Riemann and Lebesgue integrals have been introduced and studied (see for example, [2-9, 13-15, 17, 18, 25, 29-34, 36, 37, 39-43, 54, 55, 58, 68]).…”

“…The study of non-additive set functions and nonlinear integrals has received a wide recognition because of its applications in many domains such as: potential theory, subjective evaluation, optimization, economics, decision-making, data mining, artificial intelligence, and accident rate estimations (e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). In the literature, there are several methods of integration for (multi)functions based on extensions of the Riemann and Lebesgue integrals.…”