## 2 Material and Methods
### Multi-Criteria Decision-Making: Foundations
Decision- makers compare the relative importance of criteria, sub-criteria, or alternatives two at a time, using a scale of 1 to 9, where 1 indicates equal significance and 9 indicates extreme importance of one element over the other [49]. These comparisons are used to construct a comparison matrix for each level of the hierarchy. A priority vector is calculated from these matrices, representing each element's relative weight. Additionally, AHP includes a consistency check to ensure that the judgments made in the pairwise comparisons are logically consistent. A consistency index (CI) is calculated, and if the value is less than 0.1, the consistency is considered acceptable; otherwise, the judgments should be reviewed and adjusted. Finally, the priority weights are combined to calculate the overall score for each alternative, helping to identify the best option based on the defined criteria [38]. In parallel, TOPSIS operates on the principle that the chosen alternative should have the shortest distance from the positive ideal solution (PIS), which represents the best possible scenario, and the farthest distance from the negative ideal solution (NIS), representing the worst possible scenario [41]. This dual consideration of the ideal and anti-ideal solutions makes TOPSIS particularly effective in handling trade-offs among multiple conflicting criteria, providing a balanced evaluation of each alternative. The method is straightforward and intuitive, normalising data, calculating distance measures, and ranking other options based on their relative closeness to the ideal solution. The calculation process of TOPSIS involves different steps, according to [37; 50]. First, the decision matrix lists all alternatives and their performance scores across various criteria. Each criterion's values are then normalised to transform them into dimensionless numbers, facilitating comparison. This normalisation is typically performed using the Euclidean distance formula. Next, the weighted normalised decision matrix is formed by multiplying the normalised values by their corresponding criterion weights, reflecting each criterion's relative importance. The positive ideal solution (PIS) and negative ideal solution (NIS) are then determined. The PIS consists of the best values for each criterion (maximum for benefits and minimum for costs), while the NIS consists of the worst values (minimum for benefits and maximum for costs). The Euclidean distances to the PIS and NIS are calculated for each alternative. Finally, the relative closeness of each alternative to the ideal solution is computed, and the other options are ranked accordingly. The alternative with the highest relative closeness to the PIS is considered the best choice. Therefore, the MCDSS for identifying the most suitable PV sets employs both AHP and TOPSIS methods in parallel to enhance the overall reliability and effectiveness of the decision-making process. Utilising these methods simultaneously allows for a comprehensive evaluation of their performance, helping to identify which method best determines the optimal photovoltaic system according to the criteria specified by the user. The following section explores the steps in developing and implementing this decision support system.