# Conceptual Design Evaluation Considering Confidence Based on Z-AHP-TOPSIS Method
## 4 Results
Figure 8: Conceptual design of four kinds of waste containers in the kitchen. (**a**) Design 1 (**b**) Design 2 (**c**) Design 3 (**d**) Design 4. \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 & (0.25, 0.25, 0.74) & (0.23, 0.69, 1.15) & (0.21, 0.36, 0.50) & (0.25, 0.41, 0.57) & (0.02, 0.034, 0.047) \\ Design 2 & (2.98, 3.83, 3.83) & (1.41, 1.97, 2.53) & (0.07,0.21,0.36) & (0.57, 0.74, 0.74) & (0.007, 0.007, 0.02) \\ Design 3 & (0.25, 0.74, 1.23) & (0.16, 0.49, 0.81) & (0.29, 0.41, 0.52) & (0.05, 0.14, 0.24) & (0.012, 0.019,0.027) \\ Design 4 & (0.35, 0.35, 1.04) & (0.69, 1.15, 1.61) & (0.36, 0.50, 0.64) & (0.41, 0.57, 0.74) & (0.034, 0.047, 0.061) \\ \hline \hline \end{tabular}  
* Step 4.3. Determination of the PIS and NIS.
* Drawing on Equations (19) and (20), the PIS and NIS are acquired as follows: \[I^{+}=\{(2.98,3.83,3.83),(1.41,1.97,2.53),(0.36,0.50,0.64),(0.57,0.74,0.74),(0. 034,0.047,0.061)\}\] \[I^{-}=\{(0.25,0.25,0.74),(0.16,0.49,0.81),(0.07,0.21,0.36),(0.05, 0.14,0.24),(0.007,0.007,0.02)\}\] \[\text{Step 4.4. Calculation of the closeness degree.}\]  
\end{table} 
Table 5: Z-AHP weighted decision matrix. The closeness degrees \(C_{i}\) can be computed by Equations (21)-(24), which are illustrated in Table 6.  
The closeness degrees of each design are calculated, and the ranking of the design possibility is determined as in Table 7.  
For managers, the degree of self-confidence is lower than that of designers, so the three-scale self-confidence is extended to five-scale self-confidence to express the situation of lack of self-confidence, as shown in Figure 9. The linguistic term which means the confidence in evaluation is \"weak\" is assigned (0, 0, 0.1667, 0.3333) TpFN, \"unlikely\" is assigned (0.1667, 0.3333, 0.5) TFN, \"neutral\" is assigned (0.3333, 0.5, 0.6667) TFN, \"likely\" is assigned (0.5, 0.6667, 0.8333) TFN, and \"absolutely\" is assigned (0.6667, 0.8333, 1, 1) TpFN over the total range of [0, 1]. The Z-AHP pairwise comparison matrix and the Z-TOPSIS decision matrix of managers are shown in Tables 8 and 9. The closeness degrees and the ranking of the design possibility is determined as in Table 10. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Criterion** & **Design 1** & **Design 2** & **Design 3** & **Design 4** \\ \hline \(d_{z}^{+}\) & 9.179 & 10.715 & 6.327 & 12.462 \\ \(d_{i}^{-}\) & 9.009 & 13.865 & 6.596 & 12.894 \\ \(C_{i}\) & 0.495 & 0.564 & 0.510 & 0.509 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The closeness degrees of the designs. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Design Possibility** & \(C_{i}\) & **Rank** \\ \hline Design 1 & 0.495 & 4 \\ Design 2 & 0.564 & 1 \\ Design 3 & 0.510 & 2 \\ Design 4 & 0.509 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Ranking of the design possibility. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Design Possibility** & \(C_{i}\) & **Rank** \\ \hline Design 1 & 0.495 & 4 \\ Design 2 & 0.564 & 1 \\ Design 3 & 0.510 & 2 \\ Design 4 & 0.509 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The fuzzy comparison matrix of managers for the criteria. Figure 9: Five-scale self-confidence linguistic terms.