## 4 Results
### Algorithms Selection
Regarding Criterion#6, the \"In-house software\" is scored as \"1\" since in this case the algorithm is not available. All the other scores actually refer to real number of software packages that implement the algorithm. If the algorithm is available as a Matlab 3 rd party code it scores 2. The ideal solution is \(V^{+}\) = [0.0056, 0.0104, 0.1606, 0.022, 0.030] and the anti-deal solution is \(V^{-}\) = [0.0398, 0.0729, 0.0178, 0.1175, 0.0055, 0.0033]. Table 14 presents the results of the application of the TOPSIS method. The last column of the matrix shows the ranking. The comparison of the algorithms indicate that SL is the most efficient followed by the K-medoids. In all criteria, the SL scores sufficiently. Also, the hierarchical algorithms UPGMA, UPGMC and MVM are highly ranked. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **C\#1** & **C\#2** & **C\#3** & **C\#4** & **C\#5** & **C\#6** \\ \hline K-means & 3 & 1 & 1 & 8.31 & 3 & 9 \\ Modified K-means\#1 & 3 & 1 & 9 & 978.81 & 3 & 1 \\ Modified K-means\#2 & 3 & 1 & 1 & 15.93 & 3 & 1 \\ WFA K-means & 3 & 1 & 1 & 8.44 & 3 & 1 \\ IWFA K-means & 3 & 1 & 9 & 713.80 & 3 & 1 \\ Hopfield K-means & 3 & 1 & 1 & 49.53 & 3 & 1 \\ minCEntropy & 3 & 1 & 9 & 691.73 & 3 & 2 \\ K-means A & 3 & 1 & 5 & 8.27 & 3 & 1 \\ K-means B & 3 & 1 & 1 & 8.16 & 3 & 1 \\ K-medoids & 3 & 1 & 7 & 9.22 & 3 & 9 \\ SL & 1 & 1 & 7 & 3.59 & 4 & 9 \\ CL & 1 & 1 & 1 & 3.69 & 4 & 9 \\ UPGMA & 1 & 1 & 5 & 3.67 & 4 & 9 \\ WPGMA & 1 & 1 & 1 & 3.68 & 4 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Evaluation scores. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scale** & **Linguistic Term in Positive Impact** & **Linguistic Term in Negative Impact** \\ \hline
1 & Poor & Extremely strong \\
2 & _Intermediate value_ & _Intermediate value_ \\
3 & Moderate & Very strong \\
4 & _Intermediate value_ & _Intermediate value_ \\
5 & Strong & Strong \\
6 & _Intermediate value_ & _Intermediate value_ \\
7 & Very strong & Moderate \\
8 & _Intermediate value_ & _Intermediate value_ \\
9 & Extremely strong & Poor \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Decision matrix. By comparing the algorithms' categories, hierarchical algorithms are more suitable. The 2 nd place belongs to partitional algorithms and the 3 rd place to the algorithms of the rest category. Although Hopfield ANN ranks in the middle of the list, in general terms, the neural-network based algorithms is the category that ranks last. FDL and ISODATA are the least efficient algorithms. This is mainly due to the large time that is needed to extract a certain number of clusters. Therefore, it is recommended to select an algorithm that is directly fed with the number of clusters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **C\#1** & **C\#2** & **C\#3** & **C\#4** & **C\#5** & **C\#6** \\ \hline WPGMC & 1 & 1 & 1 & 3.71 & 4 & 9 \\ UPGMC & 1 & 1 & 5 & 3.73 & 4 & 9 \\ MVM & 1 & 1 & 5 & 3.70 & 4 & 9 \\ FCM & 5 & 1 & 1 & 10.91 & 1 & 6 \\ IFCM & 6 & 1 & 1 & 13.32 & 1 & 1 \\ SOM (1D) & 7 & 1 & 1 & 1148 & 3 & 6 \\ AVQ & 2 & 1 & 1 & 1244.70 & 1 & 3 \\ Hopfield & 1 & 1 & 1 & 44.69 & 3 & 5 \\ FDL & 3 & 2 & 1 & 2489.40 & 4 & 1 \\ CLA & 4 & 1 & 5 & 848.97 & 1 & 2 \\ IRC & 2 & 2 & 3 & 6.41 & 4 & 1 \\ BCEC1 & 1 & 1 & 1 & 6.83 & 4 & 1 \\ BCEC2 & 1 & 1 & 1 & 6.61 & 4 & 1 \\ CSC & 1 & 1 & 1 & 6.53 & 4 & 1 \\ SVC & 4 & 3 & 3 & 27.54 & 4 & 3 \\ ISODATA & 7 & 7 & 1 & 2489.40 & 1 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: _Cont._