# A Blockchain-Based Quality 4.0 Application for Warehouse Management System
## 5 Application
### Blockchain Application
The three decision experts (DEs) who evaluated this method were selected from various businesses according to their work and profession. The number of years that the DEs had worked in their fields of expertise was also considered. Data obtained from the business were used for evaluations. The three DEs selected for the method were evaluated through an online survey using the linguistic variables given in Table 4 below. The weights given by DEs are shown as Pythagorean Fuzzy Numbers (PFN). Then, the PFS method was applied to calculate the criterion weight, considering the weights specified by the DEs. The CoCoSo method was used to rank the alternatives according to weighted criteria. Below, the PFS-CoCoSo method is explained in detail. The decision-making process is scientifically and logically choosing the best option. When decision experts make such decisions, it is necessary to evaluate the alternatives by considering essential criteria from various aspects for the decisions to be considered multi-criteria. In this study, decision experts used linguistic variables to apply Pythagorean fuzzy sets against uncertainties. Below are the steps of the PFS-CoCoSo method. Step 1: Creating an MCDM problem:

S = {S\({}_{1}\)S\({}_{2}\),...S\({}_{m}\)] set of alternatives, B = {B\({}_{1}\),B\({}_{2}\),...,Bn} set of criteria, P = (\(\eta_{ij}^{(k)}\)), and each i,j denotes the decision experts. The set of decision experts \(\iota DEsE=\){E\({}_{1}\), E\({}_{2}\),..., Et} is shown. Step 2: Calculating the weights of decision experts:

In the MCDM, evaluating the weights decision experts allocate is very important. k. In order to evaluate the weight of the decision expert, (b\({}_{k}\), n\({}_{k}\)) shows the rating of experts given by a decision expert. In this case, the weight value is calculated as follows:

\[\omega_{k}=\frac{\left(b_{k}^{2}+\pi_{k}^{2}\times\left(\frac{b_{k}^{2}}{b_{k} ^{2}+n_{k}^{2}}\right)\right)}{\sum_{k=1}^{i}\left(b_{k}^{2}+\pi_{k}^{2} \times\left(\frac{b_{k}^{2}}{b_{k}^{2}+n_{k}^{2}}\right)\right)},\ k=1(1)\ell,\ \omega_{k}\geq 0,\sum_{k=1}^{\ell}\omega_{k}=1 \tag{1}\]

Step 3: Creating the collective Pythagorean fuzzy decision matrix:

Linguistic values are used to form the collective Pythagorean fuzzy decision matrix. These linguistic values are given in the table below. \[\mathrm{A}=\left(\xi_{ij}\right)_{m\times n} \tag{2}\]

\[\xi_{ij}=\left(\sqrt{1-\prod_{k=1}^{\ell}\left(1-b_{k}^{2}\right)^{\omega_{k} }},\ \prod_{k=1}^{\ell}\left(n_{k}\right)^{\omega_{k}}\right) \tag{3}\]

Step 4: PFS model for calculating weights:

The following tables are used to estimate weights. As we mentioned, the first step in making a decision is to create the decision matrix. Step 5: Exact degrees are estimated. Point degrees of Pythagorean fuzzy numbers are calculated with Equation (2). Step 6: Criteria are selected. Criteria are prioritized from most important to least important according to the decision experts' preferences. Step 7: The relative importance of the average value is evaluated. The importance is estimated from the criterion listed in the second position, and the relative importance is calculated by comparing the B\({}_{j}\) criterion with the B\({}_{j-1}\) criterion. \begin{table}
\begin{tabular}{c c} \hline
**Linguistic Values** & **Pythagorean Fuzzy Numbers** \\ \hline Extremely Important (EI) & Y(0.90, 0.15, 0.409) \\ Very Very Important (VVI) & Y(0.75 0.40, 0.527) \\ Very Important (VI) & Y(0.70, 0.55, 0.456) \\ Important (I) & Y(0.60, 0.70, 0.387) \\ Less Important (LI) & Y(0.40, 0.80, 0.447) \\ Very Less Important (VLI) & Y(0.30, 0.90, 0.316) \\ \hline \end{tabular}
\end{table} 
Table 4: Linguistic values of options and degrees of decision experts. Step 8: The relative coefficient \(\text{K}_{\text{j}}\) can be calculated as follows:

\[K_{j}=\left\{ \begin{array}{cc}1,&j=1\\ s_{j}+1,&j>1\end{array} \right. \tag{4}\]

Step 9: Weights are calculated. The recalculated weight is defined as \(\rho_{\text{j}}\). \[\rho_{j}=\left\{ \begin{array}{cc}1,&j=1\\ \frac{\rho_{j}-1}{K_{j}},&j>1\end{array} \right.