# Analysis of the Relationships between Factors Contributing to Marine casualties
## 2 Materials and Methods
### Mcda  
The proposed research model takes into account the principles of multi-criteria analysis and statistical principles. The aim of this study is to determine to what extent selected factors influence the occurrence of marine casualties. The Promethee/Gaia method is an example of a method that makes this possible. The problem under investigation is defined by 'actions' (i.e., identified solutions to the problem) and 'evaluation criteria'. The study is carried out according to certain mathematical rules (the decision-maker's preferences). The Promethee II (Preference Ranking Organization Method For the Enrichment Of Evaluations And Its Descriptive Complement Geometrical Analysis For Interactive Aid) is the outranking method. It uses set of actions, a family of criteria, and preferences, and is based on the principle of pairwise comparison of the actions. The method is used to solve decision-making problems. The method examines the extent to which the actions meet the preferences, or shows how strong their influence is. The method makes it possible to determine which criteria are dominant. All criteria are taken into account simultaneously. It is also possible to evaluate each criterion separately. The method has several advantages, as follows: the criteria can be expressed in different units, there are several preference functions to choose from, and thresholds can be used to change the calculation procedure. This method was developed in 1984 by [PERSON] [23; 24]. There are several steps in the method [26], such as: defining a set of actions, defining the assessment criteria, creating a multicriteria table, determining preferences, performing calculations, and interpreting the results. It is assumed that \(A\) is a set of \(n\) actions \(A=\{a_{1},a_{2},a_{3},\ldots\,a_{n}\}\) and a consistent family of criteria \(f_{1}\) to \(f_{k}\) is \(F=\{f_{1},f_{2},f_{3}\ldots f_{k}\}\). Actions are possible solutions to a problem that need to be defined. The number of actions to be examined is finite. These actions will be assessed against each criterion. The criteria can be quantitative or qualitative. Quantitative criteria can have arbitrary units, and a scale should be created for qualitative criteria. These criteria are to be maximised or minimised. The assessment is carried out using a multi-criteria table. The rows of the table contain the actions \((a_{1}-a_{n})\), and the columns of the table contain the criteria \((f_{1}-f_{k})\). The evaluation of each action _f(a)_ is placed inside the table at the intersection of the rows and columns. The evaluations require inserting data for each action in each criterion. For example, if the criterion is'speed', the value of speed achieved by the action (e.g., in km/h) should be inserted in the table. An outranking relation is built on the basis of a preference index \(\pi\). It is used to assess the dominance of action \(a\) over action \(b\). The following Formula (1) applies:  
\[\pi(a,b)=\sum_{j=1}^{k}w_{j}\times P_{j}(a,b) \tag{1}\]  
where:  
\(\pi(a,b)\)-preference index for action \(a\) relative to action \(b\) considering all the criteria. \(w_{j}\)-the weight allocated to _j_th criterion. \(P_{j}(a,b)\)-preference function for the _j_th criterion, when action \(a\) is compared to \(b\). There are several preference functions \(P_{j}(a,b)\). The decision-maker shall choose the optimal function for every criterion. The functions are the following types: usual, level, U-shape, V-shape, linear, Gaussian. Actions will be compared \(r=f_{j}(a)-f_{j}(b)\) according to the selected function. The range of function is from 0 to 1, where 0 means no preference at all while 1 means a full preference. The linear and V-shape functions are the best for quantitative criteria (Figure 1). The thresholds (indifference threshold \(q\) and preference threshold \(p\)) are used for these functions. The thresholds are the values at which the evaluation type changes. Between thresholds, the function runs in a linear way.