# A Study of Applying Fuzzy Theory in Simulation-Based Education
## Methodology
### Fuzzy Analytic Hierarchy Process (FAHP)  
In this study, the geometric mean method was extended the AHP to the situation of using linguistic variables. In the FAHP methods, [PERSON] [36] used Fuzzy pairwise comparison matrices constructed by using linguistic evaluations with respect to the decision makers' judgments. In replacement of AHP definite value disadvantage, an advantage might be reached. FAHP converts the opinions of experts from previous definite values to fuzzy numbers and membership functions present triangular fuzzy numbers in paired comparisons of matrices. In this study, the three-point marking method proposed by [PERSON] [37] was used to obtain the opinions of experts, using the approach human thinking model to achieve more reasonable evaluation criteria. For example, when comparing the importance of A and B, if m is \"quite strong\" its mental feeling might be between u \"extreme strong\" and l \"little bit strong.\" The parameter l denotes the smallest possible value, m the most promising value, and u the largest possible value that describes a fuzzy event. Those who answered the questionnaire filled m in m \(\in\)[l,u], as shown in Table 2, m filled in at 5, the real situation, 3-7 can also be a possible answer. The process of FAHP [PERSON] [36] proposed is listed as following:  
1. Setting up hierarchy architecture \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Serial No** & **Fill in \(\Box\) with “V”** & \begin{tabular}{c} **Very** \\ **Unimportant** \\ \end{tabular} & \begin{tabular}{c} **Not** \\ **Important** \\ \end{tabular} & **Fair** & **Important** & \
\begin{tabular}{c} **Very** \\ **Important** \\ \end{tabular} &
\begin{tabular}{c} **Fuzzy** \\ **Number** \\ \end{tabular} \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 1: Initial evaluation values of importance. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & & & \\ \hline
**Absolute** & **Extreme** & **Quite** & **Strong** & **Slightly** & **Equal** & **Slightly** & **Quite** & **Weak** & **Extreme** & **Absolute** \\  & **Strong** & **Strong** & **Strong** & **Strong** & **Equal** & **Weak** & **Weak** & **Weak** & **Weak** & **Weak** \\ \hline
9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 & 1/2 & 1/3 & 1/4 & 1/5 & 1/6 & 1/7 & 1/8 & 1/9 \\ A & & & u & & m & & 1 & & & & & B \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Three-points marking method [37]. \"Scenario Aspects and Criteria\" went through the expert questionnaire and FDM, and based on the subject of this study, \"Evidence-based Training on the Crews Researches Management of Helicopter Flight crew\" was used to construct hierarchy model shown as Figure 1. The uppermost level was the core of this study which analyzed every \"Scenario Aspects and Criteria,\" evaluated the weight on the critical decision making process; the second level was \"Scenario/Aspect\"; and the third level was the \"Competency/Criteria\". 2. Constructing pairwise comparison matrices  
According to [PERSON]'s [36] proposed method, this study used a questionnaire survey, three-point marking method, and triangular fuzzy numbers to construct pairwise comparison matrices (supposing n elements):  
\[\widetilde{A}=\left[\overline{a}_{\text{kr}}\right]=\left[ \begin{array}{ cccc}\overline{a}_{11}&\overline{a}_{12}&\cdots&\overline{a}_{1n}\\ \overline{a}_{21}&\overline{a}_{22}&\vdots&\overline{a}_{2n}\\ \vdots&\ldots&\ddots&\vdots\\ \overline{a}_{n1}&\overline{a}_{n2}&\cdots&\overline{a}_{nm}\end{array} \right] \tag{13}\]  
where, \(\overline{a}_{\text{kr}}\), k, and r are fuzzy comparison values. (3) Fuzzy Matrix consistency  
Supposing A = [a\({}_{\text{kr}}\)] is a \"Positive reciprocal matrix,\" and \(\widetilde{\text{A}}=\left[\overline{a}_{\text{kr}}\right]\) is a fuzzy positive reciprocal matrix, then each value is presented in \(\overline{a}_{\text{kr}}=\left(\text{l}_{\text{kr}},\text{m}_{\text{kr}}, \text{u}_{\text{kr}}\right)\).