## 5 Application of ZPLTS-ELECTRE II Method in Ontology Ranking
### Comparative Analysis of ZPLTS-ELECTRE II
#### 5.3.2 Comparison with PLTS ELECTRE II  
The performance of the ZPLTS-ELECTRE II method was also compared with the PLTS ELECTRE II method [62] for the task of evaluating and ranking mental health ontologies. In the case of PLTS ELECTRE II, only PLTS data can be modeled; therefore, the decision matrix only comprises the qualitative linguistic criteria as in Table 23. Furthermore, the PLTS ELECTRE II method cannot model credibility values, and therefore, the credibility aspect was omitted. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \(O_{1}\) & \(O_{2}\) & \(O_{3}\) & \(O_{4}\) & \(O_{5}\) & \(O_{6}\) & \(O_{7}\) & \(O_{8}\) & \(O_{9}\) \\ \hline \(O_{1}\) & 0 & 0.15 & 0.27 & 0.00 & 0.71 & 0.47 & 0.41 & 0.18 & 0.87 \\ \(O_{2}\) & 0.73 & 0 & 0.27 & 0.27 & 0.71 & 0.47 & 0.41 & 0.18 & 0.86 \\ \(O_{3}\) & 0.96 & 0.92 & 0 & 0.50 & 0.43 & 0.19 & 0.38 & 0.27 & 0.94 \\ \(O_{4}\) & 0.99 & 0.97 & 0.32 & 0 & 0.76 & 0.52 & 0.45 & 0.22 & 1.00 \\ \(O_{5}\) & 0.74 & 0.89 & 0.00 & 0.27 & 0 & 0.00 & 0.14 & 0.06 & 0.62 \\ \(O_{6}\) & 0.92 & 0.89 & 0.00 & 0.46 & 0.29 & 0 & 0.33 & 0.22 & 0.91 \\ \(O_{7}\) & 0.79 & 0.94 & 0.02 & 0.12 & 0.30 & 0.06 & 0 & 0.11 & 0.61 \\ \(O_{8}\) & 0.91 & 0.83 & 0.09 & 0.23 & 0.53 & 0.29 & 0.34 & 0 & 0.95 \\ \(O_{9}\) & 0.77 & 0.56 & 0.21 & 0.31 & 0.65 & 0.41 & 0.35 & 0.12 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 21: Discordance matrix for traditional ELECTRE II. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \(O_{1}\) & \(O_{2}\) & \(O_{3}\) & \(O_{4}\) & \(O_{5}\) & \(O_{6}\) & \(O_{7}\) & \(O_{8}\) & \(O_{9}\) \\ \hline \(O_{1}\) & \(S^{f}\) & \(S^{f}\) & \(S^{f}\) & & & & \(S^{f}\) \\ \(O_{2}\) & & \(S^{f}\) & \(S^{f}\) & & & & \(S^{fThe criteria importance weights were set as 0.2 for all \(five\) criteria. Since the PLTS ELECTRE II makes use of strong, medium, and weak concordances and discordances, as well as indifference sets, the corresponding weights are also required. The strong, medium, and weak concordance weights were set as \(\omega_{\text{C}}=1\), \(\omega_{\text{C}}^{\prime}=0.9\), and \(\omega_{\text{C}}^{\prime\prime}=0.8\), respectively. The strong, medium, and weak discordance weights were set as \(\omega_{D}=1\), \(\omega_{D}^{\prime}=0.9\), and \(\omega_{D}^{\prime\prime}=0.8\), respectively. The indifference weight was set as \(\omega_{J}^{=}=0.7\). The score values for all ontologies at each criterion are shown in Table 24, and the deviation values for all ontologies at each criterion are shown in Table 25.  
Thereafter, the concordance matrix was formulated, as shown in Table 26.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{O_{i}}\) & **CoP** & **QoSD** & **DoCRNL** & **UoC** & **DoCA** \\ \hline \(\mathbf{O_{1}}\) & \(\{s_{0}(0.5),s_{1}(0.5),s_{1}(0)\}\) & \(\{s_{1}(0.5),s_{2}(0.5),s_{2}(0)\}\) & \(\{s_  
The next step was to formulate the discordance matrix. This is shown in Table 27.  
The concordance thresholds, \(c^{-},c^{0},c^{*}\), and the discordance thresholds, \(d^{0},d^{*}\), were set to \(c^{-}=0.55,c^{0}=0.70,c^{*}=0.85\) and \(d^{0}=0.25,d^{*}=0.40\). Thereafter, the strong and weak outranking graphs were built, as shown in Table 28.  
The strong and weak outranking relations were then exploited using the forward and backwards ranking procedures. The final ranking obtained was:  
\[O_{9}\succ O_{5}\succ O_{1}\succ O_{3}\succ O_{7}\succ O_{6}\succ O_{2} \succ O_{4}\succ O_{8}\]  
It can be observed that the ranking from the PLTS ELECTRE II was similar to the ranking from ZPLTS-ELECTRE II. In both rankings, ontology \(O_{9}\) was ranked first, \(O_{3}\) was ranked fourth, and the last ontology was \(O_{8}\). However, the ZPLTS-ELECTRE II method produced more tied rankings than that of the PLTS ELECTRE II method. The difference in rankings are expected due to the following issues. (1) The PLTS ELECTRE II only modeled the five qualitative linguistic criteria and was not able to combine numerical and linguistic data. (2) The PLTS ELECTRE II method was not able to model the credibility aspects of