## 3 Results and Discussion
### Multi-Criteria Decision Making with TOPSIS
#### 3.6.5 Determination of the Positive and Negative Ideal Solutions  
Compressive strength is the positive criterion, with greater compressive strength being preferable. In the positive ideal solution given in Equations (21) and (22), the maximum of 0.3357 is utilized in the relevant column of the weighted normalized decision matrix given in Equation (20). As the smaller the other values, the better, these criteria are negative criteria, and the minimum values in the relevant columns are used in the weighted normalized decision matrix given in Equation (20) in the positive ideal solution given in Equations (21) and (22). \[\text{Positive ideal solution }\left(V^{+}\right)\to V^{+}=\left(\text{max}V_{1}+\text{ min}V_{2}+\text{min}V_{3}+\text{min}V_{4}\right) \tag{21}\]  
\[V^{+}=\left(0.4420+0.0053+0.0027+0.0039\right) \tag{22}\]  
As demonstrated in Equations (23) and (24), in the negative ideal solution, the minimum value in the relevant column of the weighted normalized decision matrix (seeEquation (20)) for the compressive strength opposite to the positive was taken, while the maximum values were taken for the others. Negative ideal solutions \((V^{-})\to V^{-}=(\min V_{1}+\max V_{2}+\max V_{3}+\max V_{4})\) (23)  
\[V^{-}=(0.1074+0.1013+0.0538+0.2669) \tag{24}\]  
3.6.6. Determination of the Distances Positive and Negative Ideal Solutions  
For each alternative, positive (\(D^{+}\)) and negative (\(D^{-}\)) distances are calculated in Equations (25) and (26). \[D_{i}^{+} =\sqrt{\sum_{j=1}^{m}\left(v_{ij}-v_{j}^{+}\right)^{2}} \tag{25}\] \[D_{i}^{-} =\sqrt{\sum_{j=1}^{m}\left(v_{ij}-v_{j}^{-}\right)^{2}} \tag{26}\]  
The calculation for _PLA-FDM_ is given in Equations (27) and (28). \[D_{PLA-FDM}^{+}=\sqrt{\left(0.3357-0.4442\right)^{2}+\left(0.1013-0.0053\right) ^{2}+\left(0.0538-0.0027\right)^{2}+\left(0.0039-0.0039\right)^{2}} \tag{27}\]  
\[D_{PLA-FDM}^{-}=\sqrt{\left(0.3357-0.1074\right)^{2}+\left(0.1013-0.1013 \right)^{2}+\left(0.0540-0.0540\right)^{2}+\left(0.0039-0.2669\right)^{2}} \tag{28}\]  
The calculation for _ABS-FDM_ is given in Equations (29) and (30). \[D_{ABS-FDM}^{+}=\sqrt{\left(0.1074-0.4442\right)^{2}+\left(0.0475-0.0053 \right)^{2}+\left(0.0034-0.0027\right)^{2}+\left(0.0039-0.0039\right)^{2}} \tag{29}\]  
\[D_{ABS-FDM}^{-}=\sqrt{\left(0.1074-0.1074\right)^{2}+\left(0.0475-0.1013 \right)^{2}+\left(0.0034-0.0538\right)^{2}+\left(0.0039-0.2669\right)^{2}} \tag{30}\]  
The calculation for ABS-Inj. is given in Equations (31) and (32). \[D_{ABS-Inj}^{+}=\sqrt{\left(0.4442-0.4442\right)^{2}+\left(0.0053-0.0053 \right)^{2}+\left(0.0027-0.0027\right)^{2}+\left(0.2669-0.0039\right)^{2}} \tag{31}\]  
\[V^{+}=\left(0.4420+0.0053+0.0027+0.0039\right) \tag{22}\]0  
The results obtained by calculating for the alternatives are given in \[V^{+}=\left(0.4420+0.0053+0.0027+0.0039\right) \tag{22}\]1 \begin{table}
\begin{tabular}{c c c} \hline \hline
**Alternative** & \(\mathbf{D^{+}}\) & \(\mathbf{D^{-}}\) \\ \hline PLA-FDM & 0.1536 & 0.3483 \\ ABS-FDM & 0.3394 & 0.2732 \\ ABS-INJECTION & 0.2630 & 0.3539 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Distances to positive and negative ideal solutions. 3.6.7 Determination of the Similarity Values and TOPSIS Scores  
The similarity coefficient is calculated in Equation (33). \[S_{i}=\frac{D_{i}^{-}}{D_{i}^{+}+D_{i}^{-}} \tag{33}\]  
The TOPSIS scores are calculated for different alternatives in Equations (34)-(36). \[S_{PLA-FDM}=\frac{0.3483}{0.1536+0.3483} \tag{34}\]  
\[S_{ABS-FDM}=\frac{0.2732}{0.3394+0.2732} \tag{35}\]  
\[S_{ABS-INJ}=\frac{0.3539}{0.2630+0.3539} \tag{36}\]  
Likewise, as a result of the operations performed for 100 pieces and 1000 pieces, the following Table 9 was created. Table 9 presents the calculated TOPSIS scores and other criteria for each alternative across varying cost values. The analysis reveals that when the cost is TRY 120, the \"ABS-Injection\" alternative exhibits optimal performance, achieving the maximum TOPSIS score.