## Intelligent System to Support the Decision-Making Process in Lean Maintenance Management
### The Theory of Rough Sets to Support the Lean Maintenance Assessment
The knowledge base for the expert system was developed with PC-Shell software, which is part of the Aitech SPHINX integrated artificial intelligence suite and Aitech HybRex software. In order to test the overall quality of the classifier for all algorithms, confusion matrices (Tables 13-16) were used. These matrices were developed by comparing the results obtained by the studied companies with the result generated by the developed expert system. The classification was carried out again according to the following voting method:  
* The conformity of the actual class value and predicted class value was considered as a valid result;
* The cases when the value of the class predicted by an expert system was one class lower than the actual class value was allowed as a valid result, e.g., the actual class is a range of 30-50% and the predicted value is 10-30%. In practice, this means that an enterprise can expect projected variables to be at a minimum level of 10-30%. However, in fact, it may be higher. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{Predicted} \\ \cline{3-11}  & & **Lower than** & **30\%** & **50–70\%** & **70-85\%** & **More than** & **No. of** & **Accuracy** & **Coverage** \\ \cline{3-11}  & Lower than 30\% & 1 & 0 & 0 & 1 & 5 & 0.5 & 0.4 \\ \cline{3-11}  & 30–50\% & 0 & 1 & 0 & 2 & 5 & 0.333 & 0.6 \\ \cline{3-11} Actual & 50–70\% & 1 & 0 & 0 & 0 & 1 & 0 & 1 \\ \cline{3-11}  & 70–85\% & 2 & 0 & 0 & 3 & 0 & 8 & 0.6 & 0.625 \\ \cline{3-11}  & More than 85\% & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ \cline{3-11}  & True positive rate & 0.25 & 1 & 0 & 1 & 0 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Confusion matrix for LEM2—generated rules. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{Predicted} \\ \cline{3-11}  & & **Lower than** & **30\%** & **50–70\%** & **70-85\%** & **More than** & **No. of** & **Accuracy** & **Coverage** \\ \cline{3-11}  & Lower than 30\% & 0 & 0 & 3 & 2 & 0 & 5 & 0 & 1 \\ \cline{3-11}  & 30–50\% & 0 & 3 & 0 & 1 & 1 & 5 & 0.6 & 1 \\ \cline{3-11}  & 50–70\% & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 \\ \cline{3-11} Actual & 70–85\% & 0 & 0 & 0 & 7 & 1 & 8 & 0.875 & 1 \\ \cline{3-11}  & More than 85\% & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ \cline{3-11}  & True positive rate & 0 & 1 & 0 & 0.64 & 0.33 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Confusion matrix for the rules generated by a exhaustive algorithm. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{Predicted} \\ \cline{3-11}  & & **Lower than** & **30\%** & **50–70\%** & **70–85\%** & **More than** & **No. of** & **Accuracy** & **Coverage** \\ \cline{3-11}  & Lower than 30\% & 0 & 0 & 3 & 2 & 0 & 5 & 0 & 1 \\ \cline{3-11}  & 30–50\% & 0 & 3 & 0 & 1 & 1 & 5 & 0.6 & 1 \\ \cline{3-11}  & 50–70\% & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 \\ \cline{3-11} Actual & 70–85\% & 0 & 0 & 0 & 7 & 1 & 8 & 0.875 & 1 \\ \cline{3-11}  & More than 85\% & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ \cline{3-11}  & True positive rate & 0 & 1 & 0 & 0.64 & 0.33 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Confusion matrix for the rules generated by a genetic algorithm. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{Predicted} \\ \cline{3-11}  & & **Lower than** & **30\%** & **50–70\%** & **70–85\%** & **More than** & **No. of** & **Accuracy** & **Coverage** \\ \cline{3-11} Actual & 70–85\% & 3 & 1 & 0 & 3 & 1 & 8 & 0.75 & 1 \\ \cline{3-11}  & More than 85\% & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 \\ \cline{3-11}  & True positive rate & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Confusion matrix for the rules generated by a covering algorithm. When analyzing particular confusion matrices, it should be noted that the best results for the most common classes (30-50% and 70-85%) of the accuracy value were obtained for the rules generated by an exhaustive algorithm. The accuracy value was 0.6 and 0.875, respectively.