# Conceptual Design Evaluation Considering Confidence Based on Z-AHP-TOPSIS Method
## 4 Results

Table 2: The fuzzy comparison matrix for the defined criteria. Figure 6: Evaluation of linguistic terms. Figure 7: Three-scale self-confidence linguistic terms. Step 2.3. Calculate the weights of every criterion. By means of Equations (12)-(14), \(S_{i}\) of criterion can be calculated as follows:  
\[S_{1}=(11.40,16.91,21.53)\odot\left(\frac{1}{23.34},\frac{1}{38.01},\frac{1}{54. 83}\right)=(0.21,0.45,0.89)\]  
\[S_{2}=(4.90,9.54,14.29)\odot\left(\frac{1}{23.34},\frac{1}{38.01},\frac{1}{54. 83}\right)=(0.09,0.25,0.59)\]  
\[S_{3}=(2.90,3.09,6.84)\odot\left(\frac{1}{23.34},\frac{1}{38.01},\frac{1}{54. 83}\right)=(0.05,0.08,0.28)\]  
\[S_{4}=(2.89,4.41,6.98)\odot\left(\frac{1}{23.34},\frac{1}{38.01},\frac{1}{54. 83}\right)=(0.05,0.12,0.29)\]  
\[S_{5}=(2.26,4.06,5.20)\odot\left(\frac{1}{23.34},\frac{1}{38.01},\frac{1}{54. 83}\right)=(0.04,0.11,0.29)\]  
\(V_{j}\) of criterion can be calculated as follows:  
\[V_{1}=min\{V(S_{1}\geq S_{2},S_{3},S_{4},S_{5})\}=min\{1,1,1,1\}=1\]  
\[V_{2}=min\{V(S_{2}\geq S_{1},S_{3},S_{4},S_{5})\}=min\{0.66,1,1,1\}=0.66\]  
Figure 6:0  
Figure 6:1  
Figure 6:2  
Step 2.4. Calculate normalized weight of criteria. By means of Equation (15), the normalized weight vector is \(w\) = {0.49, 0.32, 0.08, 0.09, 0.007}. Step 3. Generation of the design possibilities. Through the analysis of customer requirements and the analysis of existing waste containers in the kitchen, four conceptual designs are obtained using the conceptual design method proposed in reference [43], as shown in Figure 6:3 Design 1 adopts dry wet separation, and an outlet is added at the bottom to discharge wastewater, as shown in Figure 8a. Design 2 uses a rotatable storage box instead of the traditional container cover, and wheels are added at the bottom to facilitate movement, as shown in Figure 8b. Design 3 adds a fixed broom and a side opening based on the traditional container, as shown in Figure 8c. Design 4, shown in Figure 8d, uses a rotatable polygon structure to realize garbage classification. However, each design has some advantages and disadvantages, so the applicability is still uncertain. Step 4. Selection of the best design. Hereafter, Z-TOPSIS is applied to identify the applicability of the design possibility concerning customer satisfaction. Step 4.1. Generation of decision matrix. Here, the decision matrix would be a (4 \(\times\) 5) matrix with four design possibilities (alternatives) and five customer requirements (criteria), as shown in Figure 6:4 \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Criterion** & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{C_{3}}\) & \(\mathbf{C_{4}}\) & \(\mathbf{C_{5}}\) \\ \hline \(C_{1}\) & (1, 1, 1) & (2.12, 3.54, 4.95) & (3.09, 3.97, 3.97) & (4.48, 6.28, 8.08) & (0.71, 2.12, 3.54) \\ \(C_{2}\) & (0.20, 0.28, 0.47) & (1, 1, 1) & (0.71, 2.12, 3.54) & (0.87, 2.60, 4.33) & (2.12, 3.54, 4.95) \\ \(C_{3}\) & (0.25, 0.25, 0.32) & (0.28, 0.47, 1.41) & (1, 1, 1) & (0.5, 0.5, 1.5) & (0.87, 0.87, 2.60) \\ \(C_{4}\) & (0.12, 0.16, 0.22) & (0.23, 0.38, 1.15) & (0.67, 2.0, 2.0) & (1, 1, 1) & (0.87, 0.87, 2.60) \\ \(C_{5}\) & (0.28, 0.47, 1.41) & (0.20, 0.28, 0.47) & (0.39, 1.15, 1.15) & (0.39, 1.15, 1.15) & (1, 1, 1, 1) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The complete fuzzy comparison matrix for the defined criteria. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Criterion**\(\rightarrow\) & \(C_{1}\) & \(C_{2}\) & \(C_{3}\) & \(C_{4}\) & \(C_{5}\) \\
**Alternative**\(\downarrow\) & \(w_{1}\)**= 0.49** & \(w_{2}\)**= 0.32** & \(w_{3}\)**= 0.08** & \(w_{4}\)**= 0.09** & \(w_{5}\)**= 0.007** \\ \hline Design 1 & (P, W) & (F, N) & (G, A) & (G, A) & (G, A) \\ Design 2 & (E, A) & (V, A) & (F, A) & (E, A) & (P, A) \\ Design 3 & (F, W) & (F, W) & (V, N) & (F, W) & (G, W) \\ Design 4 & (P, N) & (G, N) & (V, A) & (V, A) & (V, A) \\ \hline \hline \end{tabular}  
* P: Poor; F. Fair; G. Good; V: Very good; E: Excellent; W: Weak; N: Neutral; A: Absolutely.  
\end{table} 
Table 4: Decision matrix.