# Fuzzy Preference Programming Framework for Functional Assessment of Subway Networks
## 3 Methodology and Implementation
### Station Criticality Module
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Factor** & **Attributes** & **Description** \\ \hline \multirow{2}{*}{Station Size} & Number of lines & Station size reflected as number of lines and number of exits \\  & Number of exits & composing the station \\ \hline \multirow{2}{*}{Station Location} & Recreational & Station criticality based on its proximity to important locations \\  & Vitalities & where higher passenger frequency is expected \\ \hline \multirow{2}{*}{Station Nature of Use} & Intermodal Station & Station criticality derived from its nature as an intermodal station \\  & End station & Station criticality derived from its nature as an end station \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Subway Systems Criticality Attributes [25]. \[\left(m_{ij}-L_{ij}\right)\lambda w_{j}-W_{i}+L_{ij}W_{j} \leq 0\] \[\left(u_{ij}-m_{ij}\right)\lambda w_{j}+W_{i}-u_{ij}W_{j} \leq 0\] \[\text{I}=1,\,2,\,3\ldots\,\text{n}-1,\qquad\text{j}=2,\,3\ldots\, \text{n},\qquad\text{j}>\text{i}\]  
where; \(L_{ij},\ m_{ij},\ u_{ij}\) Lower, medium, and, upper bounds of triangular judgments, respectively;
5. Using expert opinion, station configuration and historical data, compute criticality scores (\(C_{R}Si\));
6. Compute the total Criticality Index per station (\(C_{R}\)) using Equation (6): \[C_{R}=\sum_{i=1}^{n}C_{R}W_{i}\star C_{R}S_{i}\] (6)  
Among the selected attributes contributing to an increased station criticality, the station location is the most diverse. Criticality index measures the respective station importance based on a number of attributes including the station location in proximity to different attractions. Accordingly, the subway map was studied in depth. All possible points of interest accessible by a subway station or a bus from a subway station were identified and grouped by their relevance to three groups of locations. A station location is either in proximity to vitalities, recreational areas, or residence areas. Table 11 lists the full description of existing points of interest in the case study subway clustered by their attraction type and grouped based on their relevance into three main groups. The criticality module phases are similar to those of the failure impacts module. First, local, and global weights are obtained using input from questionnaires and analyzed using FANP. Second, scores for different attributes are calculated and normalized based on the maximum and minimum values existent in the network understudy, where applicable. Last, scores and weights are combined to compute the final criticality index per station. In the criticality index module, normalization per score is only applicable in two attributes, number of exits and number of levels. The maximum number of exits considered is equal to the maximum number of exits in a station on the selected network for study. In our case, this number is equivalent to nine exits as concluded from the structural drawings of the stations. Maximum number of levels is calculated likewise, based on the maximum number in the network under study. The criticality index module operates on the stations system level. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Attraction Type** & **Points of Interest** & **Grouping** \\ \hline \multirow{2}{*}{Touristic Attractions} & Museums, Theatres, Touristic Centers, Playgrounds, Historical & \\  & Sites, and, Shopping Centers & \\ Sports & Amphitheaters, Gymnasiums, Stadium, and, Clubs & Recreational \\ Culture & China Towns, Cinemas, Libraries, Cemetery & \\ Transportation & Central Bus Stations, Inter-city Rail Stations & \\ Businesses & Chambers of Commerce, International District, Business District & \\ Worship Places & Churches, Mosques, Temples, Cathedral, Oratory & \\ Educational & Schools, Universities, Educational Institutions & Vital Locations \\ Governmental & City Hall, Court & \\ Health Care & Hospitals, Health Clinics, Health Institutes & \\ Residence & High, Medium, or Low Residence Regions & Residence \\ \hline \hline \end{tabular}
\end{table}