# Fuzzy Preference Programming Framework for Functional Assessment of Subway Networks
## 3 Methodology and Implementation
### Station Criticality Module
The criticality model framework is outlined in in Figure 6. Criticality of a subway station is identified by three main attributes and seven sub-attributes. The main criticality attributes are station characteristics, station location, and station nature of use. Figure 5: Proposed Subway Network Hierarchy [6]. Figure 6: Criticality Module Attributes [25]. Station characteristics is defined in terms of number of lines and number of exits per station. Station location is considered to account for increased stations' criticality due to their proximity to important location, where the service is more required and the frequency of passengers is higher (e.g., hospitals, recreational areas, and universities). A binary value is assigned per station per location; in addition, a combined location option is permitted, and hence, a station can have value in all location attributes. Station nature of use account for station importance derived from its function as an end station or an intermodal station. The attributes and sub-attributes considered in the criticality index model are summarized in Table 9. The attribute scores are computed based upon the network under examination and individual station information. The scores are obtained as shown in Table 10.  
From the definition of criticality attributes, inner and outer dependency occur between attributes analogous to those in the failure impacts module. Consequently, FANP was selected to assess criticality attributes, and a weight component is introduced in the criticality index equation to accommodate the subjective variability in the attributes weight. The score of each attribute is factor-dependent; it can be seen as a scale from less to more critical. The criticality index model is summarized in the following steps;  
1. Identify criticality attributes using literature review and experts' opinions;
2. Estimate criticality attributes weights (\(\text{C}_{\text{R}}\text{W}_{\text{i}}\)) using pairwise comparison and FANP with application to FPP;
3. Perform FPP on each comparison matrix individually to derive sets of local priorities;
4. Calculate the weights using the FPP method according to Equation (5). It is required to derive crisp priority vector \(w=(w_{1},w_{2}\ldots\ w_{n})^{T}\), such that the priority ratios \(w_{i}/w_{j}\) are approximately within the scopes of the initial fuzzy linguistic judgments provided: \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Factors** & **Attribute** & **Definition** & **Score** \\ \hline \multirow{4}{*}{Station Size} & \multirow{2}{*}{\#exits} & The increased number of exits reflects an increase in passenger capacity & Based on the maximum number of exits as defined by user \\ \cline{3-4}  & & The increased number of lines is proportional to an increased passenger capacity & Based on the maximum number of lines as defined by user \\ \hline \multirow{4}{*}{Station Nature of Used} & \multirow{2}{*}{Intermodal} & Intermodal stations pose a greater importance since a higher passenger frequency is expected. & Computed as binary value, (1) for an intermodal station and (0) if else \\ \cline{2-4}  & & End stations pose a greater importance since a higher passenger frequency is expected. & Computed as binary value, (1) for an end station and (0) if else \\ \hline \multirow{4}{*}{Station Location} & \multirow{2}{*}{
\begin{tabular}{c} Recreational \\ Residence \\ Vitalities \\ \end{tabular} } & Stations pose higher criticality due to their proximity to high passenger frequency locations. & Computed as binary value, (1) for stations located in a high capacity location and, (0) if else \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Criticality Attributes Definition and Scores [25].