# I4.0I: A New Way to Rank How Involved a Company Is in the Industry 4.0 Era
## 3 I4.0I Proposal--Industry 4.0 Index
### Methodology
#### 3.3.3. Step 3: Computing Each Technology's Value  
To limit the value of the index between 0 and 10, with 0 being the lowest value and 10 the highest value, each technology was weighted using Equation (1), where:  
* \(L\) = technology's level;
* \(n_{L}\): position of the technology inside its own level;
* \(W_{n,L}\): technology's truth value related to its n number;
* \(N_{L}\): total number of technologies on the respective level;
* \(T_{L}\): calculated by Equation (2), it allows the \(W_{n,L}\) to represent the truth value of each technology. \[W_{n,L}=\frac{n_{L}/N_{L}}{T_{L}} \tag{1}\]  
\[T_{L}=\sum_{n_{L}=1}^{N_{L}}\frac{n_{L}}{N_{L}} \tag{2}\]  
As an example, we show the calculation of the truth value related to each generic technology presented in Table 3, where it is possible to see that the respective level is composed of four technologies, which gives the \(N_{L}\) number. Hence, using Equation (2), we can calculate \(T_{L}\) to this general level:  
\[T_{L}=\sum_{n_{L}=1}^{4}\frac{n_{L}}{N_{L}}=\frac{1}{4}+\frac{2}{4}+\frac{3}{4 }+\frac{4}{4}\]  
\[T_{L}=2.5\]  
Replacing the \(T_{L}\) value calculated above in Equation (1), we can determine the \(W_{n,L}\) related to each technology. * Technology A: \[W_{2,3}=\frac{2/4}{2.5}\] \[W_{2,3}=0.2\]
* Technology B: \[W_{4,3}=\frac{4/4}{2.5}\] \[W_{4,3}=0.4\]
* Technology C: \[W_{3,3}=\frac{3/4}{2.5}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(L\) & \(n_{L}\) & **Technology** & **Expected Market** & **Time on the** & **Logical Analysis** \\ \hline \multirow{8}{*}{3} & \multirow{2}{*}{2} & \multirow{2}{*}{Technology A} & There is not & & \multirow{2}{*}{Since BBBB} & Technology A is \\  & & & & & & required to obtain \\  & & & & information & & & technology D. \\ \cline{1-1}  & & & & B’s profit \textgreater{}C’s & \multirow{2}{*}{Since CCCC} & \multirow{2}{*}{No requirements.} \\ \cline{1-1}  & & & & & profit & \\ \cline{1-1}  & & & & & & \\ \cline{1-1}  & & & & & & \\ \cline{1-1}  & & & & & & \\ \cline{1-1} \cline{2-6}  & & & & & & \\ \cline{1-1} \cline{2-6}  & & & & & & \\ \cline{1-1} \cline{2-6}  & & & & & & \\ \cline{1-1} \cline{2-6}  & & & & & & \\ \cline{1-1} \cline{2-6}  & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Generic example of the assignment of n values. \[W_{3,3}=0.3\]
* Technology D: \[W_{1,3}=\frac{1/4}{2.5}\] \[W_{1,3}=0.1\]  
As we can see, the sum of all \(W_{n,L}\) values calculated above results in 1. Thus, considering ten levels, the maximum index will be represented by the number 10 (when the company uses all technologies related to Industry 4.0), and the minimum index will be represented by the number 0 (when the company does not use any of the technologies cited in Table 2). After computations, we can present Table 4, which consists of a complete and reorganized Table 3. Table 5 shows all technologies ranked with their respective \(L\), \(n_{L}\), and \(W_{n,L}\) values. It is important to stress that the \(W_{n,L}\) values are limited to a representation with just two decimal places; however, as the sum of all values at each level must result in 1, all necessary decimal places must be considered in the calculation. \begin{table}
\begin{tabular}{c c c c c} \hline \(L\) & \(n_{L}\) & **Technology** & **Expected Market** & **Time on the Market** & **Logical Analysis** & \(W_{n,L}\) \\ \hline  & 1 & Technology D & There is not & There is not & To obtain technology D, it is & \\  & 1 & Technology D & enough information. & enough information. & necessary to have & 0.1 \\  & 2 & Technology A & There is not & & technology A. is required & \\  & 3 & Technology C & enough information. & Since BBB & to obtain technology D. & 0.2 \\  & 4 & Technology B & C’s profit \textless{}B’s profit & Since AAAA & No requirements. & 0.3 \\ \hline  & & & B’s profit \textgreater{}C’s profit & Since CCCC & No requirements. & 0.4 \\ \hline \end{tabular}
\end{table} 
Table 4: Generic example of the assignment of n values with the respective \(W_{n,L}\) calculated value.