## 3 Results
### Optimization of the Turning Process Using a Modified PSI-TOPSIS Method
#### 3.2.3 Optimization of the Turning Process for Case 3  
In the third case, 50 alternatives were considered and randomly selected from a set of 240 in order to demonstrate the effectiveness of the modified PSI-TOPSIS method. In this case, the insert radius was considered as an input parameter, along with the other three input parameters considered in cases 1 and 2. In Figure 18, it can be seen that alternative 49 is the best choice; the closeness coefficient value is 1.000. Also, in the response table, as shown in Table 14, the optimal turning parameters are insert radius at level 2, cutting speed at level 5, feed rate at level 1, and depth of cut at level 1. Therefore, the optimal combination of input parameters in the turning process for 90 MnCrV7 steel with regard to the considered outputs is 0.8 mm insert radius, 230 m/min cutting speed, 0.5 mm depth of cut, and 0.08 mm feed rate. A higher insert radius and cutting speed and a lower depth of cut and feed rate provide the optimal combination of turning parameters that minimizes surface roughness and cutting forces. The ANOVA results (Table 15) show that insert radius is the most significant factor, with a contribution of 47.31%, followed by the depth of cut, with a contribution of 21.64%. Meanwhile, cutting speed exerts the smallest effect on the closeness coefficient compared to the other three considered parameters, with a contribution of 3.27%.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source** & **DF** & **SS** & **Adj MS** & **F-Value** & **\(p\)-Value** & **Contribution (\%)** \\ \hline \(v_{c}\) & 5 & 0.1117 & 0.02233 & 1.29 & 0.273 & 1.93 \\ \(f\) & 3 & 1.6236 & 0.54121 & 31.28 & 0.000 & 28.12 \\ \(a_{g}\) & 4 & 2.1870 & 0.54675 & 31.60 & 0.000 & 37.88 \\ Error & 107 & 1.8515 & 0.01730 & & & \\ Total & 119 & 5.7738 & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 13: ANOVA of \(C_{i}\) value for case 2.  
Figure 17: Main effects plot for mean \(C_{i}\) for case 2.  
As observed in the main effects plot for the mean output responses, as shown in Figure 19, the surface roughness (\(R_{a}\)) and cutting forces (\(F_{c}\), \(F_{p}\), and \(F_{f}\)) decrease with an increasing value of the insert radius of the cutting tool, while they increase with increasing values of the feed rate and depth of cut. This is due to the fact that an increase in the feed rate and depth of cut leads to an increase in the cross-section of the chip, which results in higher cutting forces and worse surface roughness. In order to minimize surface roughness and cutting forces, a cutting speed in the range of 130 m/min to 230 m/min should be avoided in the turning process for 90 MnCrV7 steel. In Figure 19, it can be seen that the lowest values of all considered outputs (\(R_{a}\), \(F_{c}\), \(F_{p}\), and \(F_{f}\)) were achieved at a cutting speed of 230 m/min. This cutting speed value is the optimal value for all three considered cases. Therefore, based on all of the above, it can be noted that the proposed PSI-TOPSIS method effectively provides very good results, regardless of the number of considered alternatives.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Input Parameter** & **Level 1** & **Level 2** & **Level 3** & **Level 4** & **Level 5** & **Level 6** & **Optimal Level** \\ \hline \(r_{i}\) & 0.4498 & 0.7696 & - & - & - & - & 2 \\ \(v_{c}\) & 0.6018 & 0.6578 & 0.4713 & 0.4514 & 0.6908 & 0.6169 & 5 \\ \(f\) & 0.7734 & 0.6997 & 0.4937 & 0.4783 & - & - & 1 \\ \(a_{p}\) & 0.8674 & 0.6382 & 0.5957 & 0.5342 & 0.4324 & - & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 14: Response table for mean \(C_{i}\) for case 3.  
Figure 18: Closeness coefficient for each alternative for case 3.