## 2 Materials and Methods
### Fuzzy Logic  
When managing vessel traffic, the VTSO determines priority by determining the risk of the traffic situation. In general, this task is expressed as a collision risk analysis. However, for a VTSO that has to manage the efficiency and safety of the entire VTS area rather than the situations of individual vessels, the priority for vessel traffic management must be determined from a perspective different to the collision risk analysis of the vessel operator [27]. In other words, it should be possible to quantify and express a myriad of intermediate states, not simply the two perspectives of \"dangerous\" or \"safe\", and consequently determine the ranking according to the degree. In a specific navigation area, vague perceptions such as \"keep a very close distance\" and \"there is little time for collision avoidance\" are determined by the subjective judgment of the VTSO. However, fuzzy logic can be used to quantify and express unclear values [28], as it provides a method to mathematically deal with the fuzziness of linguistic expressions. Fuzzy logic has been developed by many researchers since its introduction by [PERSON] in 1965 [29]. Its use allows expressing the extent to which a certain element a belongs to set A from 0 (no membership) to 1 (full membership), rather than classifying it as to whether it belongs to set A (true) or not (false). Figure 6 shows a schematic of the FIS inference process. In fuzzification, the input data are received in the form of crisp data, and the extent to which they belong to each suitable fuzzy set is determined. In the rule evaluation, the fuzzy input is received and applied to the antecedent of the fuzzy rule to obtain a number representing the evaluation result of the antecedent, which is then applied to the membership function of the latter. Subsequently, the fuzzy set of all rules for the latter is merged into one. Further, in defuzzification, the integrated output fuzzy set is output as a single number through the Center of Gravity (COG). Fuzzy logic begins with defining a membership function. In this study, fuzzy logic was used to calculate the existing collision risk index to define the membership function. Assuming that the prioritization index for ship traffic management can be expressed using two factors, CPA and TCPA, among the various parameters of the ship navigation data, the model is constructed. In the model by [PERSON] and [PERSON], the risk levels of the two vessels were quantified, as shown in Table 2, and divided into four risk levels for each [10]. In addition, in studies that defined collision avoidance rules, collision avoidance action was applied between vessels according to the classification of the encountering relationship between ships, and the collision avoidance action was divided into four stages: collision, danger, threat, and attention [30,31]. Meanwhile, studies on ship auto-navigation using fuzzy expert systems calculated the collision risk according to two factors: CPA and TCPA [32,33]. Regarding the state variables used in the CPA and TCPA membership functions, PS, PMS, PM, PMB, and PB were selected for CPA, and NB, NM, NS, PS, PMS, PM, PMB, and PB were selected for TCPA, where S stands for small, M for medium, B for large, P for positive, and N for negative. The decision of the collision risk index (CRI) can be expressed as a two-dimensional matrix, and the CRI output by the inference rule exhibits a value between \(-1.0\) and \(1.0\). The closer the CRI is to \(1.0\), the higher the risk of collision, and a negative sign corresponds to a case wherein the TCPA is negative. [PERSON] constructed an initial fuzzy inference table by adopting the ideas of [PERSON] et al. and derived a modified membership function table using an adaptive network fuzzy inference system (ANFIS) based on the data collected through navigation simulation results [11,34]. In this study, an initial fuzzy inference table was constructed, as listed in Table 3, with reference to the results of previous studies.