# User Satisfaction Survey on Public Transport by a New PAHP Based Model
## 4 Results of the Parsimonious AHP Survey
The calculation of the results has also been exactly the same as in the conventional AHP process for the attributes of the third, non-Parsimonious level. In **Step 6**, the priorities for all the criteria have been obtained (the comprehensive evaluation was done by employing Formula (6)) within the interval we have repositioned all other criteria scores. \[u(\text{Approachability})=0.169+\frac{0.221-0.169}{0.096-0.052}\;(0.058-0.052)=0. 169+\frac{0.052}{0.044}\;(0.006)=0.176\]  
\[u(\text{Reliability})=0.221+\frac{0.610-0.221}{0.149-0.096}\;(0.102-0.096)=0.221 +\frac{0.389}{0.053}\;(0.006)=0.427\]  
Consequently, the ranking order has been kept for all criteria in the Parsimonious level. Before determining the final scores in the decision, the original decision structure (see Figure 2) has to be rebuilt. Based on this, the final Parsimonious scores have to be normalized by their position in the original hierarchy. For instance, the Parsimonious score of Approachability, Directness, Time availability, Speed and Reliability have to be normalized to 1 (Table 7). Moreover the other, non-Parsimonious levels and criteria scores have to be attached to the decision. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**CR = 0.00258**} & **Information before Travel** & **Directness** & **Mental Comfort** & **Scores** & **Rank** \\ \hline Information before travel & 1 & 0.278 & 1.675 & 0.221 & 2 \\ Directness & 3.597 & 1 & 2.911 & 0.610 & 1 \\ Mental comfort & 0.597 & 0.344 & 1 & 0.169 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The PCM of the reference criteria gaining the normalized scores of (\(u(c_{\text{ks}})\)). The other normalized scores for the elements in the Parsimonious level which obtained by the PAHP approach are calculated based on Formula (6). As following (Table 8):  
\[u(\text{Time availability})=0.169+\frac{0.221-0.169}{0.096-0.052}\left(0.078-0.05 2\right)=0.2\]  
\[u(\text{Speed})=0.169+\frac{0.221-0.169}{0.096-0.052}\left(0.056-0.052\right)=0. 174\]  
\[u(\text{Physical comfort})=0.221+\frac{0.610-0.221}{0.149-0.096}\left(0.116-0.096 \right)=0.368\]  
\[u(\text{Safety of travel})=0.221+\frac{0.610-0.221}{0.149-0.096}\left(0.111-0.096 \right)=0.331\]  
\[u(\text{Perspicuity})=0.221+\frac{0.610-0.221}{0.149-0.096}\left(0.103-0.096 \right)=0.272\]  
\[u(\text{Info during travel})=0.169+\frac{0.221-0.169}{0.096-0.052}\left(0.057-0. 052\right)=0.169+1.182\left(0.005\right)=0.175\]  
Based on this, the final decision scores and ranking can be obtained and the multi-level PAHP problem can be solved. We note again that the first level in the decision structure is obviously equals to the AHP scoring. According to the PAHP approach outcomes, the final scores and the criteria ranking are presented in Tables 9 and 10. Table 10 exhibits the final scores for the second level of the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Criteria** & **Direct Evaluation** & **Rank** &
\begin{tabular}{c} **Parsimonious Scores** \\ **(\(u(c_{kp})\))** \\ \end{tabular} \\ \hline Approachability & 0.058 & 8 & 0.176 \\ _Directness_ & 0.149 & 1 & 0.610 \\ Time availability & 0.078 & 7 & 0.200 \\ Speed & 0.056 & 10 & 0.174 \\ Reliability & 0.124 & 2 & 0.427 \\ Physical comfort & 0.116 & 3 & 0.368 \\ _Mental comfort_ & 0.052 & 11 & 0.169 \\ Safety of travel & 0.111 & 4 & 0.331 \\ Perspicuity & 0.103 & 5 & 0.272 \\ _Information before travel_ & 0.096 & 6 & 0.221 \\ Information during travel & 0.057 & 9 & 0.175 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The direct evaluation by passengers and the final Parsimonious scores (\(u(c_{kp})\)) of the criteria in level 2.