## 5 Conclusions  
Decision making is an indispensable element of our private and professional lives. Such decisions may concern, for example, acceptance of a technical solution, choosing the best solution among the available options, or choosing the most appropriate control systems in conditions of uncertainty and risk. The above issues are related to making engineering decisions involving the search for optimal solutions; therefore, the task must be a so-called well-defined problem. Thus, the designer is faced with the task of formulating an optimization problem that includes formulating criteria for the assessment of decisions, actions, or effects of controlling any system. For this reason, the paper proposes a method for selecting the number of criteria to assess the quality of decisions taken, which can be used in modeling decision-making situations, especially in engineering issues related to controlling complex systems. In such cases, depending on the time horizon and external conditions, making the optimal decision may involve difficulties, and is often associated with the risk of making a mistake. Therefore, when designing the control device, the designer must formulate a vector criterion function that allows the analysis of many variants in a limited time. Formulated in this work:  
* The conditions of completeness, coherence, and nonredundancy that must be met by the vector criterion adopted for the assessment of the decision situation, ensuring the selection of the number of scalar criteria in the vector criterion relevant to the modeled decision situation;
* A theorem of introducing the scalar criterion into the vector criterion, and a theorem of reducing the number of criteria in the vector criterion for variables and constant user preferences, ensuring the selection of such a number of criteria that user preferences are taken into account in the modeled decision situation;
* Claims about increasing or reducing the dimension of the vector criterion allowed in order to create a method of forming the vector criterion for any decision task in which the scalar criteria with their confidence levels are specified. The presented method was used to formulate a decision task for the needs of a marine anticollision system. A specific vector criterion based on the formulated method ensures the selection of safe control in a collision situation of the ship's movement and is optimal in the economic aspect. The application of the presented method to model the decision situation requires defining a set of scalar criteria assessing the quality of the decision made. If these are measurable values, then the relative accuracy \(\alpha_{n,2}\) can be determined, e.g., resulting from the measurement accuracy as well as the confidence level of exceeding the limit value \(\alpha_{n,3}\). The confidence level \(\alpha_{n,1}\) is a subjective quantity determined by experts. It should be emphasized that this parameter is one of the three confidence levels used to assess the confidence of a given scalar criterion. In addition, the subjectivity of the adopted values can be minimized by increasing the number of experts participating in the assessment. The adopted method ensures finding a vector criterion function, the form of which excludes its further modification in accordance to the presented theorems. The solution obtained in the presented example is intuitively correct because in the final form, the vector criterion takes into account the most important indicators assessing traffic safety, i.e., the smallest approach distance and the time remaining to reach the smallest approach distance, as well as the two most important indicators related to traffic economics, i.e., lost time and loss roads for anticollision maneuver. The remaining indicators taken into account during the selection procedure of the optimal vector indicator are based on indicators that were adopted in its final form, and thus it seems intuitive to not take them into account.