## 2 Methodology
### Stage 1--Problem Formulation Stage
Variable d\({}_{1}\) describes the possibility of hazards to operation to surface navigation, variable d\({}_{2}\) describes the existence of a possibility of hazards to surface and underwater navigation, and variable d\({}_{3}\) describes the possibility of hazards to surface and underwater navigation. Additionally, available technologies were: remotely operated underwater vehicle (ROV), unmanned aerial vehicle (UAV), light detection and ranging (LIDAR), autonomous underwater vehicle (AUV), satellite-derived bathymetry (SDB), and multibeam echosounder (MBES). They have a set of specific characteristics which the manufacturer determines. Once survey area data are obtained and the available technology is known, a reduced elimination binary matrix can be created. A hydroographer fills the elimination matrix based on survey area data and performances of available technologies. Regarding the knowledge about survey area data, these are data that the hydroographer must be aware of for planning surveying. Additionally, as far as knowledge of technologies' performances, these data vary depending on the model, and they are available from the manufacturer. Therefore, filling the elimination matrix is a simple process, and it is performed by a hydroographer based on available data. Since all available technologies are not suitable for all survey areas, the elimination matrix is used for rapid and transparent elimination of inappropriate technologies. Hence, the values from the elimination matrix represent the input in the decision tree model. The basic reduced binary elimination matrix is shown in Figure 2.  
Figure 2: Reduces binary elimination matrix with corresponding submatrices. The rows in Figure 2 represent characteristics and sub characteristics of the survey area (described in Figure 1), and the columns \(Al_{1},\;Al_{2},Al_{3},\ldots,Al_{k}\) represent available technologies. The technologies are represented as alternatives that come into consideration. The reduced binary elimination matrix's element \(x_{kz}\) indicates the binary value (0 or 1) of \(k\)-th alternatives \(A_{k}\) with respect to the \(z\)-th characteristic survey area \(Ch_{z}\), Expressions (1) and (2):  
\[Al=\{Al_{1},\;Al_{2},Al_{3},\ldots,Al_{k}\} \tag{1}\]  
\[Ch=\{A_{1},B_{2},C_{3},\ldots,\;Z_{z}\} \tag{2}\]  
A binary filling is proposed to make the process simpler and faster. A value of 0 indicates that a particular alternative is not suitable for the specified area. Conversely, a value of 1 indicates that the observed alternative is suitable for the survey area characteristic. General characteristics of the survey area, to make the selection more precise, are divided into several sub characteristics, Expression (3):  
\[Ch=\{(a_{1},\;a_{2},\cdots,a_{j}),\;(b_{1},b_{2},\cdots,b_{m}),\ldots(z_{1},z_ {2},\cdots z_{z})\} \tag{3}\]  
where \(\big{(}a_{1},a_{2},\cdots,a_{j}\big{)}\) are sub characteristics of \(A_{1}\), \((b_{1},b_{2},\cdots,b_{m})\) are sub characteristics of \(B_{2}\), and \((z_{1},z_{2},\cdots,z_{z})\) are sub characteristics of \(Z_{z}\). In practice, the number of characteristics in the matrix can be smaller than is suggested in Figure 2. If, for example, there is no possibility of hazard (characteristic D), then it can be dropped from the matrix and not considered. Each characteristic under consideration usually has only one sub characteristic. For example, if characteristic C is observed, the maximum depth is generally known, and the characteristic C is represented with only one sub characteristic. In contrast, the characteristic E (seabed type) of the survey area does not have to be unambiguously defined. For example, the bottom part may be rocky, while the other part may be heavy vegetation. In such a case, two sub characteristics of characteristic E are considered. All available alternatives and sub characteristics defined for a particular characteristic of the survey area define submatrices. The total number of submatrices depends on the total number of characteristics of the hydrographic survey area.