## 4 Analysis and Discussion of Results
In other words, railway operators tend to prefer large capacity rail sections to the detriment of the bottlenecked ones, with clear impacts on idleness measurements. This is also in line with the industrial practice from the perspective that the bottlenecked rail sections normally faced the issue of constraints in the number of tracks available or the capacity of the signalling/power supply system. These issues significantly affect the number of trains that they can accommodate, and rail operators obviously will avoid them and choose the rail sections with good infrastructure. Figure 4: (**a**) (top-left) presents the correlograms for the normalized attributes. (**b**) (top-right) presents attributes’ distances to ideal solutions. (**c**) (bottom) presents attributes’ hesitant membership function value. The sign reversal of these relationships with respect to the distance to the ideal solutions \(u\) confirms that the idle bottlenecked rail sections present less operational slacks or flexibility to accommodate additional cargo demand, in comparison to the idle-large capacity rail sections. In fact, the higher the former, the closer to its operational limits (ideal solutions). Conversely, the higher the latter, the further to its ideal solutions. This overall picture indicates that the Brazilian railways have already been stressed with regard to their bottlenecks at the rail section level. This provided an indication of the industrial practices/policies implemented by the Brazilian government. Over the period 1997-2004, there had been in total R$ 44 billion in private investment in the railroad [40]. In addition, the Brazilian government invested R$ 17.6 during 1997-2016, and both the private investment and government investment aimed to solve the bottlenecked issue in the railway system. Our analysis suggests that the level of investment from both the government and the private sector should be further increased. In addition, there are two models in existence in the Brazilian railway industry: vertically integrated and infrastructure concesions. Differences between these two models result in bottlenecks in freight operations, and the diversity of rules makes the corrections on the issue of bottlenecks more difficult and increases the reliance on government investment [41]. However, the same cannot be said in terms of stressing them towards higher levels of utilization in large capacity sections. In terms of hesitant membership functions \(h\), this explains why the bottleneck percentage of the idelness pair is higher (higher certainty with respect to the operational limits) than the installed capacity-idelness pair (lower certainty as regards the flexibility limits to accommodate additional cargo demand). In short, there is more certainty on what rail sections are not capable of delivering than the other way around. Figure 5 reports on the normalized attribute weights obtained after removing the positive and negative biases inherent to the measurements in **x**, **u**, and **h**. Readers should recall that these weights are obtained as the bounded averages of the unbiased distances to the ideal solutions in terms of the respective unbiased membership degrees. Readers may note that the normalized attribute weights obtained after positive bias removal are more balanced than those obtained after negative bias removal. This suggests that the key to better rail section performance in Brazil relies on a balance among bottleneck, minimum curve radius, and installed capacity; criteria that presented practically the same positive weights. These three different determinants provide important implications for industrial practice from the perspective that installed capacity seems fixed in the short term, but through the fixing of bottlenecks by relevant investment from the government and the private sector, this can be further expanded, while in terms of the minimum curve radius, it is important due to the fact that it is closely related to the construction cost and operations cost.