## 3 Case Design
\right]\]  
\[\widetilde{R}_{3}=\left[ \begin{array}{ccccc}0.20&0.30&0.40&0.10&0.00\\ 0.21&0.16&0.53&0.11&0.00\\ 0.21&0.32&0.32&0.16&0.00\\ 0.35&0.39&0.17&0.09&0.00\end{array} \right]\]  
\[\widetilde{R}_{4}=\left[ \begin{array}{ccccc}0.18&0.41&0.36&0.05&0.00\\ 0.19&0.43&0.29&0.10&0.00\\ 0.35&0.39&0.17&0.09&0.00\end{array} \right]\]  
\[\widetilde{R}_{5}=\left[ \begin{array}{ccccc}0.33&0.50&0.08&0.08&0.00\\ 0.18&0.41&0.36&0.05&0.00\\ 0.33&0.38&0.25&0.04&0.00\end{array} \right]\]  
\[\widetilde{R}_{6}=\left[ \begin{array}{ccccc}0.33&0.50&0.08&0.08&0.00\\ 0.18&0.41&0.36&0.05&0.00\\ 0.33&0.38&0.25&0.04&0.00\end{array} \right]\]  
\[\widetilde{R}_{7}=\left[ \begin{array}{ccccc}0.33&0.50&0.08&0.08&0.00\\ 0.18&0.41&0.36&0.05&0.00\\ 0.33&0.38&0.25&0.04&0.00\end{array} \right]\]  
\[\widetilde{R}_{8}=\left[ \begin{array}{ccccc}0.33&0.50&0.08&0.08&0.00\\ 0.18&0.41&0.36&0.05&0.00\\ 0.33&0.38&0.25&0.04&0.00\end{array} \right]\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Upper-level Factor** & **Lower-level Factor** & **Weight** & \(\boldsymbol{CR}\) \\ \hline \multirow{3}{*}{Creativity (\(U_{4}\))} & Innovation (\(u_{41}\)) & 0.22 & \multirow{3}{*}{0.02} \\  & Uniqueness (\(u_{42}\)) & 0.229 & & \\  & Avant-garde (\(u_{43}\)) & 0.352 & & \\  & Personal style (\(u_{44}\)) & 0.199 & & \\ \hline \multirow{3}{*}{Economy (\(U_{5}\))} & Product material (\(u_{51}\)) & 0.164 & \multirow{3}{*}{0.01} \\  & Assembly approach (\(u_{52}\)) & 0.201 & & \\ \cline{1-1}  & Cost estimation (\(u_{53}\)) & 0.167 & & \\ \cline{1-1}  & Spatial arrangement (\(u_{54}\)) & 0.178 & & \\ \cline{1-1}  & Simplicity (\(u_{55}\)) & 0.29 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._The fuzzy evaluation matrix can be obtained from the above-mentioned procedures. The comprehensive evaluation and operation were carried out by implementing Model 4 of the fuzzy synthetic method. This synthetic method only requires carrying out normalization of \(w_{i}\). Therefore, there is no need to normalize the results obtained from the fuzzy comprehensive evaluation. The operations are as follows for the low-level evaluation:  
\[\text{Functionality factor}:\ \overline{B}_{1}=\widetilde{W}_{1}\bullet \overline{R}_{1}=\Big{[}\ 0.263\ \ \ 0.397\ \ \ 0.300\ \ \ 0.044\ \ \ 0.00\ \Big{]},\] \[\text{Structure factor}:\ \overline{B}_{2}=\widetilde{W}_{2}\bullet \overline{R}_{2}=\Big{[}\ 0.341\ \ \ 0.311\ \ \ 0.307\ \ \ 0.041\ \ \ 0.00\ \Big{]},\] \[\text{Aesthetics factor}:\ \overline{B}_{3}=\widetilde{W}_{3}\bullet \overline{R}_{3}=\Big{[}\ 0.266\ \ \ 0.307\ \ \ 0.321\ \ \ 0.110\ \ \ 0.00\ \Big{]},\] \[\text{Creativity factor}:\ \overline{B}_{4}=\widetilde{W}_{4}\bullet \overline{R}_{4}=\Big{[}\ 0.248\ \ \ 0.419\ \ 0.227\ \ \ 0.045\ \ 0.107\ \Big{]},\] \[\text{Economy factor}:\ \overline{B}_{5}=\widetilde{W}_{5}\bullet \overline{R}_{5}=\Big{[}\ 0.293\ \ \ 0.369\ \ 0.239\ \ 0.099\ \ 0.00\ \Big{]}.\]  
It is known from Table 2 that the weights of the high-level factors can be determined, and the high-level judgment matrix is as follows:  
\[\overline{R}^{*}=\left[ \begin{array}{c}\overline{B}_{1}\\ \overline{B}_{2}\\ \overline{B}_{3}\\ \overline{B}_{4}\\ \overline{B}_{5}\end{array} \right]=\left[ \begin{array}{ccccc}0.263\ \ \ 0.397\ \ \ 0.300\ \ \ 0.044\ \ \ 0.00\\ 0.341\ \ \ 0.311\ \ \ 0.307\ \ \ 0.041\ \ \ 0.00\\ 0.266\ \ \ 0.307\ \ \ 0.321\ \ \ 0.110\ \ \ 0.00\\ 0.248\ \ \ 0.419\ \ \ 0.227\ \ \ 0.107\ \ \ 0.00\\ 0.293\ \ \ 0.369\ \ \ 0.239\ \ \ 0.099\ \ \ 0.00\end{array} \right].\]  
Therefore, the result of the high-level fuzzy comprehensive evaluation is  
\[\overline{C}=\widetilde{W}\bullet\overline{R}^{*}=\Big{[}\ 0.288\ \ \ 0.346\ \ \ 0.289\ \ \ 0.080\ \ 0.00\ \Big{]}.\]  
As for the processing of evaluation indices, typical methods in common use are maximum degree of membership and weighted averaging. Weighted averaging can turn vague values into definite values. This is the so-called defuzzification effect. The purpose of defuzzification is to transform the final data or results with vague properties into definite values and data.