## 4 Example of Formulating a Vector Criterion  
The issue of choosing the number of criteria used to evaluate decisions is a significant problem in many decision-making tasks. In the paper, as an example of using the presented method of selecting the number of criteria, we will consider the task of choosing a vector criterion in a complex object control system in a conflict situation. The presented principles of selection of the vector quality criterion will be used to formulate a decision task for the needs of designing the ship's anticollision system. This task can be formulated as follows:  
The number of criteria in the vector quality of control indicator used to select the optimal safe trajectory in a collision situation by the ship's anticollision system should be chosen, assuming:  
- the criterion should take into account the aspect of traffic safety and economics,  
- gyro compass accuracy \(\pm\) 3%,  
- accuracy of log indications \(\pm\) 4%,  
- radar accuracy when measuring distances \(\pm\) 4%,  
- radar accuracy at speed measurement \(\pm\) 5%,  
- radar accuracy when measuring bearing \(\pm\) 3%. Analyzing the process of controlling a sailing object in a collision situation and taking into account the requirements for anticollision systems, we come to the conclusion that the assessment of control should be made in terms of traffic safety, and this aspect of control is the most important. In the set of safe controls, we can look for solutions that provide optimal control regarding the economic aspect. For the above reasons, the selection of optimal control will be made on the basis of a vector quality indicator which will include both safety-related criteria and criteria related to traffic economics [2; 3; 4; 5]. Among the criteria for evaluating control from the standpoint of security, one can distinguish the following criteria:  
- The shortest approach distance \(D_{min}^{j}\) determined by the equation:  
\[F_{1}(x)=D_{min}^{j}=\frac{y_{j}V_{wy}^{j}-x_{j}V_{wx}^{j}}{V_{w}^{j}} \tag{18}\]  
where \(V_{w}^{j}\) is the relative speed of the \(j\)-th object relative to its own ship, \(V_{wx}^{j},\ V_{wy}^{j}\) are the relative coordinates of relative speed, \(x_{j},\ y_{j}\) are the appropriate coordinates of the location of the \(j\)-th object in the rectangular coordinate system associated with its own ship;  
- Time remaining until reaching the closest distance is determined by the equation:  
\[F_{2}(x)\ =T_{Dmin}^{j}=\frac{y_{j}V_{wy}^{j}+x_{j}V_{wx}^{j}}{\left(V_{w}^{j} \right)^{2}} \tag{19}\]Collision risk indicator is determined by the equation: \[F_{3}(x)=r_{j}=\frac{D_{b}T_{b}}{\sqrt{\varepsilon_{1}\big{(}D_{min}^{j}T_{b} \big{)}^{2}+\varepsilon_{2}\big{(}D_{b}T_{Dmin}^{j}\big{)}^{2}}}\] (20) where \(D_{b}\) is the distance from the ship to the \(j\)-th object, \(T_{b}\) is the safe time to complete the maneuver, \(\varepsilon_{1},\varepsilon_{2}\) are weight factors depending on the type of body of water, degree of visibility at sea, and dynamic length and width of the ship and draft; Collision risk angle is defined by the equation: \[F_{4}(x)=\delta_{0}^{j}=\ \text{arcsin}\frac{D_{min}^{j}}{D_{j}}\] (21) where \(D_{j}\) is the distance from the ship to the \(j\)-th object, Aspect of the \(j\)-th object is determined by the equation: \[F_{5}(x)=A_{j}=q_{j}^{0}=\pi+N_{j}-\psi_{j}\] (22) where \(N_{j}\) is the bearing on the \(j\)-th object, \(\psi_{j}\) is the course of the \(j\)-th object.