## 5 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**PEO** & **LL** & **C** & **L** & **T** & **EC** & **P** & **SC** & **CS** & **TC** & **KC** & **GS** \\ \hline
**LL** & 1 & 9 & 10 & 8 & 11 & 2 & 6 & 4 & 7 & 5 & 3 \\ \hline
**C** & 6 & 1 & 5 & 2 & 9 & 3 & 8 & 4 & 11 & 10 & 7 \\ \hline
**L** & 7 & 6 & 1 & 5 & 3 & 2 & 4 & 8 & 11 & 10 & 9 \\ \hline
**T** & 8 & 3 & 5 & 1 & 6 & 4 & 10 & 2 & 9 & 11 & 7 \\ \hline
**EC** & 8 & 6 & 2 & 4 & 1 & 5 & 3 & 7 & 11 & 9 & 10 \\ \hline
**P** & 2 & 8 & 4 & 7 & 10 & 1 & 3 & 5 & 11 & 9 & 6 \\ \hline
**SC** & 5 & 10 & 3 & 8 & 4 & 2 & 1 & 6 & 11 & 7 & 9 \\ \hline
**CS** & 6 & 8 & 11 & 5 & 10 & 7 & 9 & 1 & 3 & 4 & 2 \\ \hline
**TC** & 5 & 9 & 11 & 6 & 10 & 7 & 8 & 3 & 1 & 4 & 2 \\ \hline
**KC** & 5 & 9 & 11 & 8 & 10 & 6 & 7 & 3 & 2 & 1 & 4 \\ \hline
**GS** & 5 & 9 & 10 & 7 & 11 & 6 & 8 & 2 Based on the ranking matrices, the agreement between matrices of the three data similarity measures are computed. Table 9 shows the mutual agreement between every pair of measures in their measuring of the similarity between a particular PEO and the other PEOs. It also shows the average agreement (last row) between every pair of similarity measures across all of them. Obviously, CS indicates full agreement with ED for LL PEO and with MD for L and SC PEOs. Interestingly, the CS measures show higher agreement with ED and MD than the agreement between ED and MD. In addition, the agreement across the three measures is computed (last column) for each PEO and across all PEOs (which is 0.49). The highest agreement between the three measures is in measuring the similarity between L and other PEOs, while the lowest agreement is in measuring the similarity between T and other PEOs. Despite the differences between the similarity measures in their evaluation of the similarity among PEOs, the overall similarity matrix, which gives an overall estimation of the similarity among PEOs based on the similarity matrices of the three measures, can be computed. However, the values of the ED similarity matrix and MD similarity matrix need to be normalized first so that their values fall in the range of 0 and 1. This can be done using the following formula:  
\[d_{Normalized}(X,Y)=\frac{1}{1+d(X,Y)} \tag{4}\]  
Then the overall similarity matrix can be computed as the average over the three matrices, as shown in Table 10. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline PEO & LL & C & L & T & EC & P & SC & CS & TC & KC & GS \\ \hline LL & 0.00 & 0.67 & 0.64 & 0.57 & 0.84 & 0.73 & 0.78 & 0.71 & 0.76 & 0.79 \\ C & 0.60 & 0.00 & 0.69 & 0.76 & 0.60 & 0.69 & 0.61 & 0.67 & 0.56 & 0.54 & 0.63 \\ L & 0.67 & 0.69 & 0.74 & 0.77 & 0.79 & 0.77 & 0.65 & 0.51 & 0.55 & 0.58 \\ T & 0.64 & 0.76 & 0.74 & 0.71 & 0.71 & 0.72 & 0.64 & 0.77 & 0.65 & 0.59 & 0.67 \\ EC & 0.57 & 0.60 & 0.77 & 0.71 & 0.71 & 0.68 & 0.75 & 0.64 & 0.52 & 0.56 & 0.53 \\ P & 0.84 & 0.69 & 0.79 & 0.72 & 0.68 & 0.70 & 0.80 & 0.78 & 0.65 & 0.70 & 0.75 \\ SC & 0.73 & 0.61 & 0.77 & 0.64 & 0.75 & 0.80 & 0.80 & 0.70 & 0.59 & 0.68 & 0.64 \\ CS & 0.78 & 0.67 & 0.65 & 0.77 & 0.64 & 0.78 & 0.70 & 0.85 & 0.83 & 0.88 \\ TC & 0.71 & 0.56 & 0.51 & 0.65 & 0.52 & 0.65 & 0.59 & 0.85 & 0.81 & 0.85 & 0.85 \\ KC & 0.76 & 0.54 & 0.55 & 0.59 & 0.56 & 0.70 & 0.68 & 0.83 & 0.85 & 0.83 & 0.83 \\ GS & 0.79 & 0.63 & 0.58 & 0.67 & 0.53 & 0.75 & 0.64 & 0.88 & 0.85 & 0.83 & 0.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Average similarity matrix. \begin{table}
\begin{tabular}{l c c c c} \hline \hline PEO & ED \& CS & ED \& MD & MD \& CS & ED \& MD \& CS \\ \hline LL & 0.73 & 0.73 & 0.73 & 0.73 \\ C & 0.82 & 0.27 & 0.18 & 0.18 \\ L & 0.82 & 0.82 & 0.11 & 0.82 \\ T & 0.45 & 0.64 & 0.27 & 0.27 \\ EC & 0.73 & 0.64 & 0.82 & 0.64 \\ P & 0.36 & 0.45 & 0.82 & 0.36 \\ SC & 0.45 & 0.45 & 0.41 & 0.45 \\ CS & 0.73 & 0.55 & 0.45 & 0.45 \\ TC & 0.64 & 0.36 & 0.64 & 0.36 \\ KC & 0.55 & 0.82 & 0.45 & 0.45 \\ GS & 0.64 & 0.82 & 0.82 & 0.64 \\ Average & 0.65 & 0.6 & 0.65 & 0.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Computed agreements between similarity measures.