# Applying the DEMATEL - ANP Fuzzy Comprehensive Model to Evaluate Public Opinion Events
## 3 Research Method
### Fuzzy Comprehensive Evaluation of Public Opinion Events  
The core of the evaluation of public opinion is to guess the developing trend and the degree of urgency of the emergent events, which is in accordance with the principles of fuzzy mathematics. The fuzzy comprehensive evaluation is based on fuzzy mathematics and applies the principle of fuzzy relationship synthesis to quantify some factors with unclear boundaries, on which it then conducts a comprehensive evaluation. Based on the indicators of the network public opinion established in the previous section and the principle of fuzzy comprehensive evaluation, the specific steps for constructing the fuzzy comprehensive evaluation model of online public opinion are as follows. Determine the set of indicators. All indicator factors together constitute the factor set written as \(U=\{U_{1},U_{2}\ldots U_{n}\}\). In the ANP network structure analysis, the indicator factors of the control layer were determined as the primary evaluation indicator factors, given as \(U_{m}=\{U_{1},U_{2},U_{3},U_{4},U_{5}\}\), and the indicator factors of the network layer were the secondary evaluation indicator factors, given as \(U_{n}=\{U_{11},U_{12},U_{21},U_{22},U_{23},U_{31},U_{32},U_{41},U_{42},U_{43}, U_{51},U_{52},U_{53}\}\). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Weighted**} & \multicolumn{1}{c}{\multirow{2}{*}{\(U_{11}\)}} & \multicolumn{1}{c}{\multirow{2}{*}{\(U_{12}\)}} & \multicolumn{1}{c}{\multirow{2}{*}{\(U_{21}\)}} & \multicolumn{1}{c}{\multirow{2}{*}{\(U_{22}\)}} & \multicolumn{1}{c}{\multirow{2}{*}{\(U_{31}\)}} & \multicolumn{1}{c}{\multirow{2}{*}{\(U_{32}\)}} & \multicolumn{1}{c}{\multirow{2}{*}{\(U_{41}\)}} & \multicolumn{1}{c}{\multirow{2}{*}{\(U_{42}\)}} & \multicolumn{1}{c}{\multirow{2}{*}{\(U_{43}\)}} & \multicolumn{1}{c}{\multirow{2}{*}{\(U_{51}\)}} & \multicolumn{1}{c}{\multirow{2}{*}{\(U_{52}\)}} & \multicolumn{1}{c}{\multirow{2}{*}{\(U_{53}\)}} \\ \multicolumn{1}{c}{**Matrix**} & & & & & & & & & & & & & & & \\ \hline \(U_{11}\) & 0.08 & 0.13 & 0.13 & 0.11 & 0.12 & 0.12 & 0.14 & 0.11 & 0.11 & 0.11 & 0.12 & 0.11 & 0.12 & 0.11 \\ \(U_{12}\) & 0.10 & 0  
Determine the weight sets. Since the indicators have different degrees of importance to the whole evaluation system, it is necessary to assign different weights to each indicator factor to distinguish its importance. According to the calculation results of the DE-ANP model, the indicator weight set was achieved, of which the weights of indicator factors at the control level were noted as m and the weights of indicator factors at the network level were noted as n, and the corresponding matrix is as follows. \[w_{n}= \begin{bmatrix}w_{11}&\cdots&w_{1n}\\ \vdots&\ldots&\vdots\\ w_{m1}&\cdots&w_{mn}\end{bmatrix} \]  
Determine the evaluation set. There are numerous topics of online public opinion information, including people's livelihood, accidents and disasters, public health, culture, education, etc. The semantic affective tendency of information has a fuzzy attribute with a clear connotation but an unclear boundary, which is in line with the basic principles of fuzzy mathematics. Regardless of the topics, the semantic affective tendencies carried by the information can be roughly summarized as positive, neutral, and negative. It is necessary to further refine the information semantic affective tendency rubric and determine the fine-grained rubric set \(V\), \(V\) = {micro, small, medium, large, extreme}, which are shown in Figure 3.  
Construct the fuzzy comprehensive evaluation sets. The advantage of fuzzy evaluation is that it can evaluate both a single factor and the total factors. If the affiliation of the i element in the factor set U corresponding to the m element in the evaluation set V was \(r_{im}\), then the single-factor evaluation result for the i element was noted as a fuzzy set: \(R_{i}=\{R_{i1},R_{i2},\ldots R_{im}\}\), with m single-factor evaluation sets \(R_{1}\), \(R_{2}\),... \(R_{m}\) as rows to form the matrix \(R_{m\times n}\).