# A Hybrid MCDM Model for Live-Streamer Selection via the Fuzzy Delphi Method, AHP, and TOPSIS
## 4 Application to Select the Optimal Live-Streamer
A questionnaire was designed based on the hierarchical framework in combination with AHP and TOPSIS. Four managers from the case study company were invited to respond to the questionnaire. The comprehensive score from group decision-making was determined by aggregating the geometric means obtained from the managers to analyze three live-streamers. In AHP, where the comprehensive score from group decision-making is obtained by aggregating geometric means, the consistency ratio of the questionnaire is less than 0.1. The pairwise comparison matrix and weight of the dimensions are shown in Table 2.  
Figure 1: Hierarchical framework to select the optimal live-streamer for shopping websites. Similarly, the weight of each criterion in a dimension was also obtained using a pairwise comparison matrix. For instance, the pairwise comparison matrix and weight of each criterion in the Individual dimension are shown in Table 3. The weight of each criterion after integration can be calculated by multiplying the weight of the criterion by the weight of the dimension to which it belongs, as shown in Table 4.  
In the TOPSIS section, the decision-makers scored the alternatives on a nine-point scale based on each criterion. A normalized evaluation matrix was created based on the evaluation matrix of opinions from the four managers obtained via the geometric mean as shown in Table 5. The normalized evaluation matrix was established based on following equation:  
\[r_{ij}=\frac{x_{ij}}{\sqrt{\sum_{i=1}^{m}x_{ij}^{2}}}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Dimension Weights** & **Criteria Weights** & **Final Weights** \\ \hline \(C_{1}\) & 0.3482 & 0.3522 & 0.1227 \\ \hline \(C_{2}\) & 0.3482 & 0.2990 & 0.1041 \\ \hline \(C_{3}\) & 0.3482 & 0.0903 & 0.0315 \\ \hline \(C_{4}\) & 0.3482 & 0.1832 & 0.0638 \\ \hline \(C_{5}\) & 0.3482 & 0.0753 & 0.0262 \\ \hline \(C_{6}\) & 0.2271 & 0.1723 & 0.0391 \\ \hline \(C_{7}\) & 0.2271 & 0.1096 & 0.0249 \\ \hline \(C_{8}\) & 0.2271 & 0.1975 & 0.0448 \\ \hline \(C_{9}\) & 0.2271 & 0.1930 & 0.0438 \\ \hline \(C_{10}\) & 0.2271 & 0.3276 & 0.0744 \\ \hline \(C_{11}\) & 0.4246 & 0.1086 & 0.0461 \\ \hline \(C_{12}\) & 0.4246 & 0.2168 & 0.0921 \\ \hline \(C_{13}\) & 0.4246 & 0.2207 & 0.0937 \\ \hline \(C_{14}\) & 0.4246 & 0.3420 & 0.1452 \\ \hline \(C_{15}\) & 0.4246 & 0.1119 & 0.0475 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Weight of each criterion after integration. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Individual** & **Work** & **Match** & **Weights** \\ \hline Individual & 1.0000 & 1.6549 & 0.7598 & 0.3482 \\ \hline Work & 0.6043 & 1.0000 & 0.5774 & 0.2271 \\ \hline Match & 1.3161 & 1.7321 & 1.0000 & 0.4246 \\ \hline The consistency ratio is 0.0044. & & & \\ \end{tabular}
\end{table} 
Table 2: Pairwise comparison matrix between the dimensions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **\(\mathbf{C_{1}}\)** & \(\mathbf{C_{2}}\)** & \(\mathbf{C_{3}}\)** & \(\mathbf{C_{4}}\)** & \(\mathbf{C_{5}}\)** & **Weights** \\ \hline \(C_{1}\) & 1.0000 & 1.3161 & 4.1618 & 2.4495 & 3.0801 & 0.3522 \\ \hline \(C_{2}\) & 0.7598 & 1.0000 & 4.5590 & 2.0000 & 2.6321 & 0.2990 \\ \hline \(C_{3}\) & 0.2403 & 0.2193 & 1.0000 & 0.4671 & 1.8612 & 0.0903 \\ \hline \(C_{4}\) & 0.4082 & 0.5000 & 2.1407 & 1.0000 & 3.6002 & 0.1832 \\ \hline \(C_{5}\) & 0.3247 & 0.3799 & 0.5373 & 0.2778 & 1.0000 & 0.0753 \\ \hline \hline \end{tabular} The consistency ratio is 0.0397.  
\end{table} 
Table 3: Pairwise comparison matrix between the criteria within the Individual dimension.