# Impact of Environmental Factors on Passenger Ride Comfort
## 4 Methodology
In the present study, different journeys can be considered as alternatives, different types of comfort as different criteria, individual comfort indices \(C_{i}\) as value functions \(v_{i}\), and the composite index \(C\) of overall ride comfort as the utility function \(v\). It should also be noted here that the methods based on MCDA have already proved effective for addressing complex decision-making processes in the broader context of transport systems, such as selecting transport modes in metropolitan areas [28]. Similarly, multi-criteria approaches have been used in the railway sector to optimise operations and infrastructure management [29]. The novel approach in this work, using the minimum function for the comfort index \(C\), reflects the authors' consideration that the overall comfort sensation is primarily determined by the least comfortable environmental factor. The proposed index C aligns with this assumption and, importantly, avoids unwanted compensation effects present in conventional approaches (such as weighted averages), which could also be used to aggregate individual comfort factors. Therefore, the chosen form of the index C is particularly well suited to cases where one environmental factor strongly contributes to discomfort. Alternative methods for calculating a synthetic index of overall comfort, which could also be considered, include the arithmetic mean of partial indices \(C_{i}\), their geometric mean, and the RMS average, as well as the corresponding weighted averages, where each comfort factor \(C_{i}\) is multiplied by a specific weight. An approach based on a weighted geometric mean of partial comfort indices has been applied in a study of ride comfort in the Montreal metro [30], with several choices of weights tested. The weighted geometric mean is also one of the two most common forms of utility functions in MCDA, alongside the weighted arithmetic mean. However, the known drawback of these forms, especially the arithmetic mean (but also the geometric mean in some cases), is the effect of compensation, where criteria with low and high ratings \(v_{i}(a)\) largely cancel out so that the resultant utility function \(v(a)\) has an intermediate value. This may not be desired in some applications, such as in the case of the evaluation of overall ride comfort. Indeed, methods based on such averages provide measures of overall comfort, which fail to correctly account for cases where a single environmental factor strongly contributes to discomfort. For example, if thermal comfort drops significantly (e.g., due to air-conditioning failure) in journey A with 4-5-1-5 ratings, the composite comfort indices defined as the arithmetic and geometric means, \(C_{av}=3.75\) and \(C_{av-gom}=3.16\), are both higher than the respective indices \(C_{av}=3\) and \(C_{av-gom}=3\) for journey B with 3-3-3-3 ratings, corresponding to an intermediate level of partial comfort for all factors. In such a case, using\(C_{av}=\left(C1+C2+C3+C4\right)/4\) or \(C_{av-geom}=\left(C1\cdot C2\cdot C3\cdot C4\right)^{0.25}\) as the index of overall ride comfort would lead to a false conclusion that journey A is more comfortable than journey B. In fact, the reverse is intuitively expected since high temperature leads to substantial discomfort in journey A, while the travel conditions are quite bearable in all considered aspects in journey B. Therefore, a different approach to defining the comfort index is necessary for a more reliable assessment of overall comfort across different journeys. The presently proposed index of comfort effectively addresses these limitations since no compensation occurs among the partial comfort indices when the minimum function is used to define this index in Equation (1). Another aspect of the present method of ride comfort evaluation that closely aligns with MCDA is the necessity to use the same rating scale for each partial comfort index \(C_{i}\), similar to the necessity to evaluate each criterion using the same rating scale for the respective function within MCDA.