## 2 Multiple-Criteria Decision-Making
### The TOPSIS Method
\begin{table}
\begin{tabular}{l c c c c c c c} \hline  & **Acc** & **RMSE** & **TP-Rate** & **TN-Rate** & **AUC** & **G-Mean** & **F-Measure** \\ \hline Bnet & **0.95** & 0.23 & 0.99 & 0.02 & **0.72** & 0.14 & 0.93 \\ NBC & 0.24 & 0.87 & 0.20 & **0.90** & 0.60 & 0.42 & 0.32 \\ logR & 0.94 & 0.23 & 0.99 & 0.02 & 0.71 & 0.14 & **0.94** \\ MLP & 0.93 & 0.24 & 0.97 & 0.20 & 0.70 & 0.44 & 0.93 \\ SVM & **0.95** & 0.22 & **1.00** & 0.00 & 0.50 & 0.00 & 0.93 \\ RBF & **0.95** & 0.22 & **1.00** & 0.00 & 0.61 & 0.00 & 0.93 \\
1 NN & 0.93 & 0.27 & 0.96 & 0.32 & 0.64 & **0.55** & 0.93 \\ RIPPER & 0.94 & 0.23 & 0.99 & 0.04 & 0.52 & 0.20 & 0.92 \\ C4.5 & 0.94 & 0.23 & 0.99 & 0.10 & 0.57 & 0.31 & 0.93 \\ randF & **0.95** & **0.21** & 0.99 & 0.16 & 0.79 & 0.40 & **0.94** \\ \hline \end{tabular}
\end{table} 
Table 10: Performance results for the Iranian database. \begin{table}
\begin{tabular}{l c c c c c c c} \hline  & **Acc** & **RMSE** & **TP-rate** & **TN-rate** & **AUC** & **G-mean** & **F-measure** \\ \hline Bnet & 0.72 & 0.43 & 0.85 & 0.42 & 0.74 & 0.60 & 0.71 \\ NBC & 0.76 & 0.42 & 0.86 & **0.51** & **0.79** & 0.66 & 0.75 \\ logR & **0.77** & **0.40** & 0.89 & 0.50 & **0.79** & **0.67** & **0.76** \\ MLP & 0.71 & 0.51 & 0.79 & 0.53 & 0.74 & 0.65 & 0.71 \\ SVM & **0.77** & 0.48 & 0.90 & 0.47 & 0.68 & 0.65 & **0.76** \\ RBF & 0.73 & 0.42 & 0.84 & 0.48 & 0.74 & 0.63 & 0.72 \\ INN & 0.67 & 0.58 & 0.76 & 0.45 & 0.61 & 0.58 & 0.67 \\ RIPPER & 0.73 & 0.44 & 0.87 & 0.40 & 0.64 & 0.59 & 0.71 \\ C4.5 & 0.72 & 0.48 & 0.83 & 0.46 & 0.67 & 0.62 & 0.72 \\ randF & 0.76 & **0.40** & **0.91** & 0.41 & 0.78 & 0.61 & 0.74 \\ \hline \end{tabular}
\end{table} 
Table 8: Performance results for the German database. \begin{table}
\begin{tabular}{l c c c c c c} \hline  & **Acc** & **RMSE** & **TP-Rate** & **TN-Rate** & **AUC** & **G-Mean** & **F-Measure** \\ \hline Bnet & **0.74** & 0.44 & 0.97 & 0.10 & 0.60 & 0.31 & 0.67 \\ NBC & 0.63 & 0.51 & 0.69 & **0.46** & 0.60 & **0.56** & 0.65 \\ logR & **0.74** & **0.43** & 0.97 & 0.10 & 0.63 & 0.31 & 0.66 \\ MLP & **0.74** & 0.44 & 0.93 & 0.20 & 0.70 & 0.43 & **0.69** \\ SVM & **0.74** & 0.52 & **1.00** & 0.00 & 0.50 & 0.00 & 0.63 \\ RBF & 0.73 & 0.44 & 0.98 & 0.02 & 0.59 & 0.14 & 0.63 \\
1 NN & 0.66 & 0.59 & 0.77 & 0.34 & 0.56 & 0.52 & 0.66 \\ RIPPER & 0.73 & 0.44 & 0.94 & 0.15 & 0.55 & 0.38 & 0.68 \\ C4.5 & 0.72 & 0.44 & 0.94 & 0.13 & 0.57 & 0.35 & 0.67 \\ randF & 0.73 & 0.44 & 0.91 & 0.22 & **0.64** & 0.45 & **0.69** \\ \hline \end{tabular}
\end{table} 
Table 9: Performance results for the [PERSON] database. metrics for this application domain because they choose optimal methods independently of the class distribution and the misclassification costs [44; 47]. Keeping these questions in mind, elicitation of weights was based on the subjective procedure of the fuzzy approach proposed by [PERSON] and [PERSON] [45] and then the weights were normalized in the interval \([0,1]\) (see the last row of Table 11). Table 12 reports the ranks and the preference values of the prediction models given by TOPSIS and PROMETHEE. Note that the higher the ranking, the better the classifier. The analysis of the ranks produced by these two MCDM techniques reveals that the random forest and logistic regression algorithms were the best performing algorithms since both TOPSIS and PROMETHEE agreed with their decisions. Paradoxically, despite the conclusions drawn by some authors [17], the SVM appeared as one of the worst alternatives for credit granting decision problems according to the ranks produced by TOPSIS and PROMETHEE; this situation could be explained by the employment of unsuitable performance assessment criteria, while the MCDM techniques could correct such misleading results. In addition, the naive Bayes classifier and the 1 NN decision rule were among the worst ranked classification algorithms. Despite the ranks achieved with TOPSIS and PROMETHEE being rather similar to one another, a composite ranking score was further defined as the mean of the preference values of both techniques for each prediction method \(i\).