# Multicriteria Analysis of Alternative Marine Fuels in Sustainable Coastal Marine Traffic
## 3 Materials and Methods
### The Application of Multicriteria Approach  
Multicriteria decision analysis (MCDA) is a method that is broadly used in order to solve complex problems, which are often consist of contradictory criteria and different quantitative and qualitative measures [33; 34]. The authors in [35] defined MCDA as an \"umbrella term to describe a collection of formal approaches which seek to take explicit account of multiple criteria in helping individuals or groups explore decisions that matter\". Due to the fact that the process of alternative marine fuel selection considers multiple aspects and the involvement of different stakeholders, we decided to apply the multicriteria approach. It is widely used when analyzing complex tasks and it found its application in many different fields, such as marine spatial data infrastructure [36], decision support to policy selection [37], energy issues and sustainable development of the energy supply systems [38; 39], and urban road infrastructure maintenance planning [40]. This approach has already been used for marine fuels [17; 41]. The authors in [41], by applying MCDA, assessed the prospects for seven alternative fuels, including biofuels. In their assessment, various groups of Swedish stakeholders were involved (industry representatives from shipowners, fuel producers, government authorities, and engine manufacturers). The ranked criteria cover four aspects: economic, environmental, technical, and social. Their results showed that different stakeholders have different priorities. From a government perspective, the most important criterion is the environment, while industry representatives ranked economic criteria as the most important. The multicriteria decision analysis process is based on several steps: In the first step, a decision problem is defined along with the main goal. In the second step, a set of objectives and corresponding criteria is defined. The objectives and criteria are assigned with weights representing their degree of importance. A set of alternatives is defined in the further step, and values representing their particular performance are attributed to each criterion and goal. Finally, alternatives are ranked according to their overall performance. It is important to highlight that the purpose of the multicriteria analysis is to provide support during the decision-making process, rather than choosing only one solution. According to the stakeholder's interests, any new criteria for evaluation of alternatives may be added and appraised through the multicriteria analysis method. The Analytic Hierarchy Process (AHP), one of the most widely used multicriteria decision-making tools developed by [PERSON] [42], is used for assigning weights to elements at each level of the hierarchy, in order to define and prioritize key elements in the evaluation of each alternative. Elements of each level are compared to each other using a pairwise comparison, creating a comparison matrix with a range depending on the number of elements at each level. In order to define the matrix, pairwise comparisons can be translated into scale values where the preferences of the decision makers are expressed through [PERSON]'s nine-point ranking scale, S = (1, 2, 3, 4,5, 6, 7, 9), used to describe the intensity of the mutual relationship from equal to extreme. Values 1, 3, 5, 7, and 9 represent the main scoring values, and 2, 4, 6, and 8 represent intermediate values. After defining the matrix of pairwise comparisons, the vector of relative weight is estimated. The validity of the comparisons is evaluated by calculating the consistency ratio (CR):  
\[\text{CR }=\frac{\text{CI}}{\text{RI}} \tag{1}\]  
where RI is the random consistency index and CI is the consistency index defined as CI = \((\lambda_{\text{max}}-n)/(n-1)\), where \(\lambda_{\text{max}}\) is the maximum eigenvalue. Once the criteria and corresponding weights are determined, the performance of each alternative is evaluated in comparison to all criteria and objectives.