# Fuzzy Preference Programming Framework for Functional Assessment of Subway Networks
## 3 Methodology and Implementation
### Failure Impacts Module  
Determining failure impacts presents a challenging problem to researchers and industry experts due to the uncertainties associated with the different financial, social, and operational aspects of the impacts. While direct financial impacts of a subway failure can be estimated based on historical data, calculating failure impacts for intangible factors, such as social, economic, and even indirect cost of failure in monetary terms is difficult and does not yield accurate results due to the high level of uncertainty and subjectivity associated with these factors. Indirect impacts of failure in subway stations include numerous attributes such as service disruption, delay of passengers, reputation loss, and revenue deficit, in addition to other socio-economic impacts. Therefore, determining failure impacts is crucial because it provides public authorities with a framework for clustering network components based on their relative importance. The triple bottom line approach is used to determine failure impacts on a multi-perspective level. A station is composed of a number of elements operating simultaneously. Based on the location of the element and its nature, the element failure might cause total, partial, or no station closure. This suggests failure impacts are element-dependent, hence, the failure impacts module is developed on elements level and aggregated upwards to the stations and network levels of a subway hierarchy using the parallel-series network modeling approach. Based on literature review and expert feedback, failure impacts were grouped into financial, social, and, operational impacts. It is noted that some factors are independent and follow two different perspectives simultaneously. Figure 1 demonstrates the main criteria and attributes considered in the failure impacts module. Financial impacts of failure represent the direct tangible impacts measured in terms of cost of maintenance, repair, or replacement of the failed component(s). This is in addition to the expected revenue loss due to partial or total station failure or service interruption. Operational impacts are those involving managerial decisions, such as time to repair and ease of providing alternative. Social impacts are the direct social failure impacts incurred by the customers. They are measured in terms of the user traffic frequency, interruption rate, and service continuation. The magnitude of the social impacts is directly proportional to the number of users using this station and the adjacent businesses to which the station connects. Examining failure impacts revealed a level of interdependency between attributes and sub-attributes. This is the type of interdependency precisely modeled by ANP. Furthermore, these attributes convey a degree of fuzziness and subjectivity derived from using experts' opinion; thus, the FANP will be utilized to develop the model. FANP addresses the interdependency inherent in the relation between these factors; in addition, it accounts for the uncertainty caused by the use of expert opinions due to the topic subjectivity. Failure impacts considered in this research are quite diverse; therefore, they were measured using indices to facilitate the comparison between the expected impacts and to highlight the areas of higher impact. FANP with application to FPP was used as the main analysis tool to obtain the failure impacts criteria weights. The membership function maps crisp inputs in the universe of discourse to degrees of membership within a certain interval, which is usually [0, 1]. Then, the degree of membership specifies the extent to which a given element belongs to a set or is related to a concept. A fuzzy extension of the five-point fundamental scale proposed by [PERSON] will be used in the pairwise comparison process. Triangular fuzzy numbers were selected for their wide applicability and ease of comprehension by decision makers.