## 4 Results
As discussed in Section 3, the remarkable change between segmentations reflects the effects of technical or operational developments, new requirements, or specific arrangements on the vessel traffic being analyzed. Thus, the above-mentioned segmentations should not be merged. Finally, four segmentations are determined, which are the years 2000-2001, 2002-2004, 2005, and 2006-2016. The most recent segmentation, 2006-2016, is treated as the statistical time window. Based on the selected time window (2006-2016), the aleatory uncertainty of the vessel traffic accident frequency can be quantified as [0.080, 0.089] for the confidence value 0.95. For accident consequences, triangular distributions are used for the epistemic uncertainty quantification. The triangular distribution has three parameters (\(i\), \(j\), \(k\)), where \(j\) denotes the most likely value when the membership function is \(1\); \(i\) and \(k\) respectively denote the lowest and the highest possible values when the membership function equals to \(0\)[29]. The trapezoidal distribution can also be selected to quantify the epistemic uncertainty, which is another commonly used possibility distribution. In other words, there is epistemic uncertainty when selecting the possibility distribution. In order to make epistemic uncertainty as small as possible, the triangular distribution is selected in this study because less information is required to model the triangular distribution than to model the trapezoidal distribution. When there is more information about the accident consequence, it is possible to select other possibility distributions to quantify the epistemic uncertainty of the accident consequence. In the risk matrix, the accident consequence refers to the mean value of fatalities from each vessel traffic accident specifically. It can be measured in the number of fatalities per accident. In the time window (2006-2016), the lowest value, the mean value and the highest value of fatalities per accident per year can be calculated as [0.155, 0.255, 0.394], which are considered as the three parameters of the triangular distribution. According to Equation (5), the epistemic uncertainty of accident consequence can be quantified as [0.160, 0.387] for the confidence value 0.95. Since the aleatory uncertainty of the vessel traffic frequency and the epistemic uncertainty of the accident consequence are quantified for the same confidence value, they can be represented in one risk matrix, which is shown by the rectangle of solid lines in Figure 3.  
In order to verify the availability of the proposed algorithms, two comparisons have been made. The first comparison is between the common method of estimating the vessel traffic risk and the algorithm proposed to quantify uncertainties. The common method [2; 5] measures the vessel traffic accident frequency and the accident consequence by averaging the historical accident data in Table 1. Then the accident frequency and consequence are calculated as 0.095 and 0.279, respectively, which are represented by a cross symbol in Figure 3. Using the algorithm proposed to quantify uncertainties, the confidence interval of the vessel traffic accident frequency and consequence can be estimated as [0.092, 0.099] and [0.165, 0.389], which make the dashed rectangle seen in Figure 3. It should be noted that the seventeen most recent years (2000-2016) are taken as the time window in the first comparison. As can be seen in Figure 3, the cross symbol is in the dashed rectangle area. It means that the algorithm proposed to quantify uncertainties is effective and can provide more information for vessel traffic risk management. The second comparison is carried out to verify the availability of the proposed algorithm for time window selection. It is obvious in Figure 3 that the vessel traffic risk considering the time window selection is less than the vessel traffic risk calculated by all the historical accident data in the risk matrix.