## 4 Analysis and Discussion of Results  
The dataset is formed by collecting information on 7351 rail sections in Brazil from 2013 to 2016. These pieces of information are retrieved from the Network Statement, which is completed every year by each railway operator and disclosed by ANTT (2022) [3]. They are incorporated as a longitudinal data panel, where performance levels would increase by year-on-year improvements in infrastructure and variations in idleness levels. The errors (railway sections with a length or installed capacity equal to zero) and the missing data that disqualify the railway section for the purposes of the study (installed capacity, minimum curve radius, ramp, dangerous cargo, embedded equipment, type of traffic control, number of operational days per year, or linked capacity not informed) are excluded. The railway sections with an installed capacity equal to zero are considered to be one hundred percent idle. While information errors and missing values have been excluded from the analysis, epistemic uncertainty may still exist in the pieces of information collected for each rail section attribute: installed capacity, minimum curve radius, ramp, dangerous cargo, embedded equipment, type of traffic control, number of operational days per year, or linked capacity. Table 2 presents the descriptive statistics of the attributes that characterize the Brazilian rail sections. The positive and negative signs of the attributes are also presented. Correlograms for the normalized attributes (\(x\)), their respective distances to the ideal solutions (\(u\)), and their resulting hesitant membership function values (\(h\)) are depicted in Figure 4 (top-left, top-right, and bottom). Correlation pairs tend to be low to mildly moderate, with the exceptions of the following pairs: (i) percentage of idleness and bot \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Variable** & **Unit** & **Type** & **Min** & **Median** & **Mean** & **Max** & **sd** \\ \hline rail section length & (km) & – & 0.11 & 12.37 & 15.49 & 225,00 & 13.88 \\ predominant gauge & (m) & P & 1.00 & 1.00 & – & 1.60 & 0.26 \\ minimum curve radius & (m) & P & 0.00 & 225.00 & 326.80 & 5292.00 & 350.85 \\ \# operational days per year & (days) & P & 0.00 & 365.00 & 360.70 & 365.00 & 26.24 \\ installed capacity & (trains/day) & P & 0.70 & 9.10 & 15.81 & 223.20 & 19.63 \\ linked capacity & (trains/day) & P & 0.00 & 2.50 & 6.96 & 72.50 & 11.36 \\ Idleness & (trains/day) & n & \(-\)2.00 & 5.30 & 8.85 & 176.50 & 11.93 \\ Bottleneck & (trains/day) & P & 0.00 & 34.90 & 39.32 & 200.00 & 30.58 \\ linked capacity.rail section length & (trains.km/day) & P & 0.00 & 36.29 & 87.01 & 4650.75 & 203.86 \\ increasing ramp tax & (\%) & n & 0.00 & 1.00 & 0.97 & 10.00 & 0.81 \\ auxiliary power & (hp) & n & 0.00 & 0.00 & 525.40 & 12,202.00 & 1944.03 \\ percentage of idleness & (\%) & n & \(-\)100.00 & 65.10 & 60.68 & 100.00 & 30.58 \\ \hline \hline \end{tabular}  
* p = positive n = negative; idleness = [installed capacity] – linked capacity]: bottleneck = [linked capacity/installed capacity] \(\times\) 100]; percentage of idleness = [(1 – linked capacity/installed capacity) \(\times\) 100]; # rail sections = 7351 (2013–2016); negative values for idleness means over utilization of the rail section.  
\end{table} 
Table 2: Descriptive statistics on Brazilian rail sections. tlenecks (positive in \(\mathbf{x}\)); and (ii) idleness and installed capacity (negative in \(\mathbf{x}\)). These two pairs of relationships reveal the railway operators' preferences in Brazil with respect to the usage of particular rail sections. This is in line with [PERSON] and [PERSON] (2020) [2]. The lower usage of particular rail sections is in accordance with industrial practice because of the shortage of supply or demand for specific rail sections. While bottlenecks, due to different origins, constitute an obstacle to higher utilization levels of a given section; installed capacity favours increased levels of rail section utilization with minimal idleness.