## 2 Methodology
### Stage 1--Problem Formulation Stage  
The problem formulation stage begins with the diversity of the areas in which the hydrographic survey is carried out. Therefore, identifying the area's characteristics is of paramount importance. To facilitate this process, the proposed distribution of characteristics and sub-characteristics of an area is represented in Table 1.  
Table 1 is made on the basis of processed literature [21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43]. It represents the framework that the hydrographer or marine industry employees uses. The literature references are used to obtain the minimum set of survey area data. The derived minimum survey area data set together with survey technologies from the basis for binary reduction matrix elements. Each identified characteristic has been divided by a single division into sub characteristics that are mutually exclusive. From Table 1, it can be observed that the five (5) distribution characteristics are proposed to create the basics framework of the survey area and as such, form the basic elements for the binary reduction matrix. They are sorted into A, B, C, D, and E characteristics. Additionally, as it can be seen, each characteristic contains sub characteristics. Some characteristics have numerical values (A, B, and C), and some characteristics are descriptive (D and E). The proposed distribution of characteristics and sub characteristics can be applied to any area and easily supplemented with new data as needed. It has to be pointed out that not all areas are available for all technologies. Distribution A (survey area coverage per day) refers to the urgency of the hydrographic survey. For example, distribution A is divided into four (4) categories/variables: a\({}_{1}\), which covers a survey area of less than 1 km\({}^{2}\)/day; variable a\({}_{2}\), the survey area coverage between 2 and 25 km\({}^{2}\)/day; variable a\({}_{3}\), the survey area between 26 and 65 km\({}^{2}\)/day, and with variable a\({}_{4}\) covers the survey area coverage greater than 66 km\({}^{2}\)/day. The distribution B (the minimum depth to be surveyed), C (the maximum depth of a survey area), and E (seabed type) refer to the different survey techniques' performance depending on the depth and seabed type. For example, distribution B is divided into three (3) categories: variable b\({}_{1}\) concerning those technologies which can give satisfactory results of work at depths less than or equal to 1 m, variable b\({}_{2}\) represents minimum survey depths between 2 and 5 m, and the last variable b\({}_{3}\) denotes the minimum depth to be surveyed between 6 and 20 m. Distribution D (exists a possibility of hazards to operation) refers to some technologies' potential to disable survey operation and should also be considered. It contains three (3) \begin{table}
\begin{tabular}{c c} \hline \hline  & \(a_{1}\leq 1\) km\({}^{2}\)/day \\ A—survey area coverage per day & \(a_{2}\) 2–25 km\({}^{2}\)/day \\  & \(a_{3}\) 26–65 km\({}^{2}\)/day \\  & \(a_{4}\) 66 km\({}^{2}\)/day \\ \hline  & \(b_{1}\leq 1\) m \\ B—the minimum depth to be surveyed & \(b_{2}\) 2–5 m \\  & \(b_{3}\) 6–20 m \\ \hline  & \(c_{1}\leq 25\) m \\ C—the maximum depth of a survey area & \(c_{2}\) 26–45 m \\  & \(c_{3}\) \textgreater{} 45 m \\ \hline  & \(d_{1}\) exists a possibility of hazards to operation to surface navigation \\ D—exists a possibility of hazards to operation & \(d_{2}\) exists a possibility of hazards to operation to underwater navigation \\  & \(d_{3}\) exists a possibility of hazards to surface and underwater navigation \\ \hline  & \(e_{1}\) rock/ coral \\ E—seabed type & \(e_{2}\) soft (mud/sand) \\  & \(e_{3}\) heavy vegetation \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Proposed distribution of characteristics and sub characteristics of the survey area. descriptive sub characteristics/variables.