# A Blockchain-Based Quality 4.0 Application for Warehouse Management System
## 5 Application
### Blockchain Application
\tag{5}\]

Step 10: Normalized weights are calculated. Criterion weights are normalized as follows:

\[w_{j}=\frac{\rho_{j}}{\sum_{j=1}^{q}\rho_{j}} \tag{6}\]

Step 11: Normalized Pythagorean fuzzy decision-making is evaluated. \[\xi_{ij}=\left\{ \begin{array}{cc}\xi_{ij}=\left(b_{ij},n_{ij}\right),for\ benefit\ criterion\\ \left(\xi_{ij}\right)^{c}=\left(n_{ij},b_{ij}\right),for\ cost\ criterion\end{array} \right. \tag{7}\]

Step 12: Evaluation of the weighted sum model, weighted product model:

It is calculated with the weighted sum model \(\text{C}_{\text{i}}(1)\) and the weighted product model \(\text{C}_{\text{i}}(2)\) as follows:

\[\text{Ci}(1)=\sum_{j=1}^{n}w_{j}\xi_{ij} \tag{8}\]

\[\text{Ci}(2)=\sum_{j=1}^{n}w_{j}\xi_{ij} \tag{9}\]

Step 13: Balancing the scores of the alternatives:

This step involves evaluation scores to evaluate the balanced consensus score of the alternatives, which is derived as follows:

\[Q_{i}^{(1)}=\frac{S^{*}\Big{(}C_{i}^{(1)}\Big{)}+S^{*}\Big{(}C_{i}^{(2)}\Big{)} }{\sum_{i=1}^{m}\big{(}S^{*}\Big{(}C_{i}^{(1)}\Big{)}+S^{*}\Big{(}C_{i}^{(2)} \Big{)}} \tag{10}\]

\[Q_{i}^{(2)}=\frac{S^{*}\Big{(}C_{i}^{(1)}\Big{)}}{minS^{*}\Big{(}C_{i}^{(1)} \Big{)}}\frac{+S^{*}\Big{(}C_{i}^{(2)}\Big{)}}{minS^{*}\Big{(}C_{i}^{(2)} \Big{)}} \tag{11}\]

\[Q_{i}^{(3)}=\frac{\gamma S^{*}\Big{(}C_{i}^{(1)}\Big{)}+(1-\gamma)S^{*}\Big{(} C_{i}^{(2)}\Big{)}}{\gamma maxS^{*}\Big{(}C_{i}^{(1)}\Big{)}+(1-\gamma)S^{*} \Big{(}C_{i}^{(2)}\Big{)}} \tag{12}\]

Here, \(\gamma\) is the decision strategy coefficient. Step 14: The general situation is evaluated. The consensus index Qi is evaluated to indicate the importance of the alternative as follows:

\[Q_{i}=\Big{(}Q_{i}^{(1)}+Q_{i}^{(2)}+Q_{i}^{(3)}\Big{)}^{1/3}+\frac{1}{3} \Big{(}Q_{i}^{(1)}+Q_{i}^{(2)}+Q_{i}^{(3)}\Big{)} \tag{13}\]

The priorities of the alternatives are calculated by increasing the degrees of the consensus index Q. In applying the PFS-CoCoSo method, Tables 4 and 5 show the weights given by decision experts as linguistic values. The information in Table 6 was created using the values in Table 7 and using Equation (1). The weights of three decision experts on the alternatives for different criteria are shown in Table 8. The weight of each criterion created by decision experts using PFS is given in Table 9. Each decision expert was asked to select the importance of each criterion. Using Equations (4)-(6), decision experts ranked all available features from first to last. Based on PFS, the criterion with the highest importance was given first place, while the criterion with the most minor importance was given last place. Overall rankings obtained by decision experts were estimated. The weights of all criteria are shown as wj in Table 10. Using Equations (10)-(13), the results of the PFS-CoCoSo model were estimated and shown in Table 11. According to the results obtained according to the consensus index Qi value, the order was S1 \(>\) S2 \(>\) S3 \(>\) S4. In line with these results, it was seen that the best option was the Q-4.0 model (S1) we developed. The software used by the company where the application was made (S2) ranked second. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Decision Expert** & **Linguistic Values** & **Pythagorean Fuzzy** & **Weight** \\ \hline E1 & Important (I) & Y(0.60, 0.70, 0.387) & 0.2325 \\ E2 & Very Very Important (VVO) & Y(0.75, 0.41, 0.518) & 0.4370 \\ E3 & Very Important (VI) & Y(0.70, 0.55, 0.456) & 0.3398 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Decision experts’ weights for evaluating options.