## 4 Results: Example Design of Parent-Child Interactive Exercise Bike
### Scheme Evaluation  
The panel of specialists who participated in the demand-gathering stage were requested to assess the design scheme to confirm its viability using the fuzzy comprehensive assessment method. The precise procedures are detailed below:  
1. Use the criteria layer indicators from the hierarchical model in Figure 3 as the assessment factor set \(P\), where \(P=(P_{A},P_{B},P_{C},P_{D})\), and the sub-criteria layer indicators as the second-level factor set \(V_{i}=(V_{1},V_{2},V_{3},\ldots,V_{n})(i=1,2,3,\ldots,n)\). 2. Use the Likert five-point scale as the assessment grade standard, and set the evaluation set \(\text{R}=(\text{R}_{1},\text{ R}_{2},\text{ R}_{3},\text{ R}_{4},\text{ R}_{5})=(\text{Very Satisfied},\text{ Satisfied},\text{ Average},\text{ Dissatisfied},\text{ Very  
Figure 12: Appearance design. Source: own processing. Dissatisfied). Give distinct assessment scores to relevant assessment levels after value assignment: \(r=(90,80,70,60,50)\). 3. Assessment professionals were asked to evaluate the performance of every scheme indicator and acquired the fuzzy comprehensive assessment matrix \(E\) for each indication: \[E_{A}= \begin{bmatrix}3&2&1&0&0\\ 3&1&1&0&1\\ 4&1&0&1&0\\ 3&1&1&1&0\end{bmatrix} \] (11) \[E_{B}= \begin{bmatrix}4&1&0&1&0\\ 5&1&0&0&0\\ 3&2&1&0&0\\ 2&2&1&1&0\\ 2&3&0&0&1\end{bmatrix} \] (12) \[E_{C}= \begin{bmatrix}3&2&1&0&0\\ 3&1&0&2&0\\ 2&1&0&3&0\\ 4&1&0&1&0\\ 2&1&2&1&0\end{bmatrix} \] (13) \[E_{D}= \begin{bmatrix}5&0&1&0&0\\ 4&2&0&0&0\\ 3&1&2&0&0\end{bmatrix} \] (14)  
The matrices \(E_{A}\), \(E_{B}\), \(E_{C}\), and \(E_{D}\) are obtained by normalizing the matrices, respectively:  
\[E_{A}= \begin{bmatrix}0.5000&0.3333&0.1667&0&0\\ 0.5000&0.1667&0.1667&0&0.1667\\ 0.6667&0.1667&0.1667&0\\ 0.5000&0.1667&0.1667&0.1667&0\end{bmatrix}  \tag{15}\]  
\[E_{B}= \begin{bmatrix}0.6667&0.1667&0&0.1667&0\\ 0.8333&0.1667&0&0&0\\ 0.5000&0.3333&0.1667&0&0\\ 0.3333&0.3333&0.1667&0.1667&0\\ 0.3333&0.5000&0&0&0.1667\end{bmatrix}  \tag{16}\]  
\[E_{C}= \begin{bmatrix}0.5000&0.3333&0.1667&0&0\\ 0.5000&0.1667&0&0.3333&0\\ 0.3333&0.1667&0&0.5000&0\\ 0.6667&0.1667&0.1667&0\\ 0.3333&0.1667&0.3333&0.1667&0\end{bmatrix}  \tag{17}\]  
\[E_{D}= \begin{bmatrix}0.8333&0&0.1667&0&0\\ 0.6667&0.3333&0&0&0\\ 0.5000&0.1667&0.3333&0&0\end{bmatrix}  \tag{18}\]  
Utilizing the weighted average fuzzy operator, via the synthesis operation of the index weights in Tables 4-7 and the corresponding evaluation matrix \(E\), the evaluation weight vector \(Z\) of the criterion layer index of the design scheme can be determined as follows:  
\[Z_{A}=W_{A}\times E_{A}= \begin{pmatrix}0.5355&0.2319&0.1313&0.0734&0.0281 \end{pmatrix}  \tag{19}\]\[Z_{B}=W_{B}\times E_{B}=\left(0.5158\quad 0.2910\quad 0.0641\quad 0.0990\quad 0.0301\right) \tag{20}\]  
\[Z_{C}=W_{C}\times E_{C}=\left(0.4417\quad 0.2217\quad 0.1283\quad 0.2084\quad 0\right) \tag{21}\]  
\[Z_{D}=W_{D}\times E_{D}=\left(0.6660\quad 0.1457\quad 0.1883\quad 0\quad 0\right) \tag{22}\]  
Consequently, it is possible to create a fuzzy comprehensive evaluation matrix of target layer indicators:  
\[Z_{P}= \begin{bmatrix}Z_{A}\\ Z_{B}\\ Z_{C}\\ Z_{D}\end{bmatrix} = \begin{bmatrix}0.5355&0.2319&0.1313&0.0734&0.0281\\ 0.5158&0.2910&0.0641&0.0990&0.0301\\ 0.4417&0.2217&0.1283&0.2084&0\\ 0.6660&0.1457&0.2319&0&0\end{bmatrix}  \tag{23}\]  
Compute the comprehensive evaluation vector for the parent-child interactive exercise bike design scheme:  
\[Q=W_{P}\times Z_{P}=\left(0.5323\quad 0.2347\quad 0.1189\quad 0.0955\quad 0.0189\right) \tag{24}\]  
Finally, the total assessment score for the scheme is calculated:  
\[L=Q\times r=81.6726 \tag{25}\]  
Expert scholars were invited to evaluate the design scheme of a home entrance disinfectant device using the fuzzy comprehensive evaluation method [32]. The final score of the scheme was 83.45, falling within the range of 80-90, indicating that the scheme has relatively good feasibility [32].