# Applying the DEMATEL - ANP Fuzzy Comprehensive Model to Evaluate Public Opinion Events
## 4 Empirical Analysis
### Fuzzy Comprehensive Evaluation  
The set of fuzzy comprehensive evaluation weights was constructed in accordance with the calculation results of the DEMATEL\(-\)ANP model, where the control layer weights were \(\omega=\{0.2,0.3,0.1,0.12,0.28\}\), and the network layer weights were \(\omega_{1}=\{0.57,0.43\}\), \(\omega_{2}=\{0.38,0.33,0.29\},\omega_{3}=\{0.73,0.27\},\omega_{4}=\{0.76,0.12,0. 12\}\),and \(\omega_{5}=\{0.34,0.32,0.34\}\). Following the affiliation principle and according to the determined rubric set \(V=\{\)micro, small, medium, large, extreme\(\}\), the affiliation of the rubric set took the value \(V=(0.2,0.4,0.6,0.8,1.0)\). Based on the determined set of factors, a single-factor evaluation matrix \(R_{i}\) was constructed. \[R_{1} = \begin{bmatrix}0.93&0.06&0.03&0&0\\ 0.85&0.10&0.03&0.01&0\end{bmatrix} \] \[R_{2} = \begin{bmatrix}0.84&0.09&0.06&0.01&0\\ 0.86&0.06&0.04&0.03&0.01\\ 0.74&0.21&0.02&0.03&0\end{bmatrix} \] \[R_{3} = \begin{bmatrix}0.72&0.18&0.09&0.01&0\\ 0.68&0.30&0.02&0&0\end{bmatrix} \] \[R_{4} = \begin{bmatrix}0.82&0.11&0.07&0&0\\ 0.44&0.17&0.23&0.04&0.12\\ 0.28&0.12&0.46&0.10&0.04\end{bmatrix} \] \[R_{5} = \begin{bmatrix}0.81&0.16&0.01&0.02&0\\ 0.78&0.12&0.04&0.03&0.03\\ 0.72&0.16&0.10&0.02&0\end{bmatrix} \]  
The new \(B_{i}\) fuzzy evaluation matrix was obtained using the fuzzy synthesis of each single-factor evaluation matrix in Formula (6), where \(B_{1}=\{0.90,0.08,0.03,0.0\}\), \(B_{2}=\{0.82,0.12,0.04,0.02,0\}\), \(B_{3}=\{0.71,0.21,0.07,0,0\}\), \(B_{4}=\{0.71,0.12,0.14,0.02,0.02\}\), and \(B_{5}=\{0.77,0.15,0.05,0.02,0.01\}\). According to the second-level fuzzy calculation method, the single-factor evaluation results of the next level were used to form the judgment matrix R of the previous level, where R is the second-level fuzzy judgment matrix \(B_{i}\). \[R= \begin{bmatrix}0.90&0.08&0.03&0&0\\ 0.82&0.12&0.04&0.02&0\\ 0.71&0.21&0.07&0&0\\ 0.71&0.12&0.14&0.02&0.02\\ 0.77&0.15&0.15&0.02&0.01\end{bmatrix}  \tag{6}\]  
The fuzzy comprehensive evaluation of the math textbook with inappropriate illustrations was \(B=\omega\times R=\{0.80,0.13,0.06,0.01,0\}\). Using Equation (5), and following \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Control Layer** & **Network Layer** & **Extreme** & **Large** & **Medium** & **Small** & **Light** \\ \hline \multirow{2}{*}{Degree of heat} & Number of issuances & 0.93 & 0.06 & 0.03 & 0 & 0 \\  & Duration of concern & 0.85 & 0.1 & 0.03 & 0.01 & 0 \\  & Number of clicks & 0.84 & 0.09 & 0.06 & 0.01 & 0 \\ Degree of quantity & Number of shares & 0.86 & 0.06 & 0.04 & 0.03 & 0.01 \\  & Number of comments & 0.74 & 0.21 & 0.02 & 0.03 & 0 \\ Degree of strength & Number of opinion leaders & 0.72 & 0.18 & 0.09 & 0.01 & 0 \\  & Network area distribution & 0.68 & 0.3 & 0.02 & 0 & 0 \\  & Negative opinion holding rate & 0.82 & 0.11 & 0.07 & 0 & 0 \\ Degree of focus & Neutral opinion holding rate & 0.44 & 0.17 & 0.23 & 0.04 & 0.12 \\  & Positive opinion holding rate & 0.28 & 0.12 & 0.46 & 0.1 & 0.04 \\  & Click growth rate & 0.81 & 0.16 & 0 & 0.02 & 0 \\ Degree of variation & Share growth rate & 0.78 & 0.12 & 0.04 & 0.03 & 0.03 \\  & Comment growth rate & 0.72 & 0.16 & 0.1 & 0.02 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Evaluation of the communication power of the math textbook illustrations. the principle of maximum subordination in fuzzy evaluation, it can be found that the math textbook with inappropriate illustrations was at the level of \"extreme\". The same method was applied to quantitatively evaluate the CNKI monopoly, shifts in the COVID-19 policy, and the crash of flight MU5735, achieving evaluation values of 0.52, 0.87, and 0.81, respectively, the specific results of which are shown in Table 8.  
The math textbook with inappropriate illustrations reached an extreme level because it is closely related to every family and every child's physical and mental health, which required an immediate response and crisis management by government education departments to change the status quo and conform to public aesthetics.