For the construction of the model and its membership function only those variables that have statistical significance are used for the development of the fuzzy model. The following are the membership functions for each of these variables.
4.3.1.1. Stress Arousal Level
Membership function for this self-report scale is developed based on the nature of the scoring instrument. The stress arousal checklist has a maximum score of 18 to evidence highest level of stress and zero to indicate no stress. Because the SACL score is found to be directly proportional to the level of stress and the scalar nature of the measurement a linear function is most appropriate.
y(x)= x 18 Where:
x = represents the score obtained for the stress dimension in the Stress Arousal Checklist (SACL)
Figure 37. SACL-Stress membership function
4.3.1.2. Workload Index (NASA TLX)
As the previous variable, the NASA TLX workload index is a self-reported instrument to assess levels of workload. The scale for such instrument is represented in percentages, describing highest level of workload with 100% rating. This workload rating instrument has been used extensively in research and associated to stress. Workload ratings have been found positively correlated to stress, therefore a simple linear curve can be used to describe the membership relation. The expression for this membership function is:
00 y(x)= x
1 Where:
x = represents the score in percentage obtained for workload
4.3.1.3. Galvanic Skin Resistance
Changes in galvanic skin resistance can be described through a decreasing sigmoid curve. Low levels of skin resistance (high levels of electricity conductance are associated with stress) are attributed to high stress conditions. Galvanic skin resistance levels can vary from a maximum of 500 KOhms to almost a minimum of cero. From the literature review it was found that a sigmoid curve fits this physiological measure and it is contained within the minimum and maximum values observed. The form of the membership function has the following expression:
( ( ))
1 1 x To y(x)=
e Where:
α = represents the amplitude of the curve and describe the growing rate 0.05 (Base 100) To = corresponds to the mean value for the mean GSR (250)
4.3.1.4. Finger Tip Temperature
Decreases on finger tip temperature are the result of vascular constriction or reduction of blood to distal extremities. As the previous objective physiological measurements, the function selected to relate this phenomena to stress has the shape of a sigmoid curve. This curve is contained within the minimum and maximum values observed. The form of the membership function has the following expression:
( ( ))
1 1 x To y(x)=
e Where:
α = represents the amplitude of the curve and describe the growing rate 0.5 To = corresponds to the mean value for the difference in temperature (7
º
F)4.3.1.5. Percentage of Maximum Heart Rate
This physiological variable describes the changes in percentage of maximum heart rate. Heart rate has been represented in previous studies with a linear membership function (Mital, A., &
Karwowski, W., 1986). Because, this measurement is a percentage of maximum heart rate a linear model can be equally used. Additionally, percentages of maximum heart rate are proportionally associated to physiological stress. A fuzzy representation of this variable has the following expression:
00 y(x)= x
1 Where:
x = represents the percentage of maximum heart rate.
Figure 41. Percentage of maximum heart rate membership function
4.3.1.6. Cortisol Level
This physiological variable describes the changes in cortisol levels. Cortisol levels are tightly associated to stress. Because, this measurement is directly proportional to the level of stress a linear curve is selected. However, for the purpose of this research cortisol levels are taken after the diurnal peak. A fuzzy representation of this variable has the following expression:
0.6 y(x)= x
Where:
x = represents the cortisol levels in g/dL.
Figure 42. Cortisol levels membership value
4.3.1.7. Number of Misses
This performance variable describes the numbers of times a warning signal was missed. This measurement grows in time and is highly dependent on workload and other stressors. Because of the nature of the variable a sigmoid curve is selected to describe the membership relation with the fuzzy set stress. The curve is contained within the minimum and maximum values observed.
This form of membership function has the following expression:
( ( ))
1 1 x To y(x)=
e Where:
α = represents the amplitude of the curve and describe the growing rate 0.5 To = corresponds to the mean value for the number of misses (9)
Figure 43. Number of misses membership function
4.3.1.8. Target Deviation
This performance variable describes the deviation error from a target. This measurement grows in time and is highly dependent on workload and other stressors. Because of the nature of the variable, a sigmoid curve is selected to describe the membership relation with the fuzzy set stress. The curve is contained within the minimum and maximum values observed. This form of membership function has the following expression:
( ( ))
1 1 x To y(x)=
e Where:
α = represents the amplitude of the curve and describe the growing rate 0.5 To = corresponds to the mean value for the deviation error (15)
4.3.1.9. Competitiveness
Membership function for this self-report scale was developed based on the scoring instrument.
The Competitiveness index has a converted maximum score of 20 to evidence highest level of competitiveness and 8 for low levels. It is assumed, based on the literature, that lowest levels of competitiveness trait bring higher levels of stress. The form of the membership function has the following expression.
1.66667 12
y(x)= x
Where:
x = represents the score obtained in the competitiveness scale instrument.
Figure 45. Competitiveness membership function
4.3.1.10. Motivation
Membership function for this self-report scale was developed based on the scoring instrument.
The Ray‘s achievement motivation scale has a maximum score of 42 for highest level of motivation and 14 for low levels. The form of the membership function has the following expression.
28 0.5 y(x)= x
Where:
x = represents the score obtained in the Ray‘s achievement motivation scale.
Figure 46. Motivation membership function
4.3.1.11. Coping
Values for this variable are obtained through a self-reported instrument. Parameters for this curve are developed based on scores from the instrument. Three dimensions for coping technique are assessed with this instrument: task focus, emotion focus and avoidance. Each dimension has a maximum value of 28 and a minimum value zero. Because coping is a mechanism that reduces stress, the curve has a negative slop and intersects the highest membership value (1) at its origin, when coping score is minimum. The form of the membership function has the following expression.
28 1 y(x)= x
Where:
x = represents the score obtained in the Coping Inventory scale
4.3.1.12. Boredom Proneness
Membership function for this self-report scale is developed based on the scoring instrument. The Boredom Proneness scale has a maximum score of 28 to indicate highly prone to boredom and 0 for the opposite condition. Study shows that the tendency to become bore, as a personal trait, is proportionally associated to levels of stress. Thus, a linear function is most appropriate to define the membership function. The form of the membership function follows the expression:
28 y(x)= x
Where:
x = represents the score obtained in the Boredom proneness scale.