## 3 Proposed Methodological Approach
### Dematel  
We propose the use of the DEMATEL method to study the interrelations among the arrays of criteria under examination. This choice is primarily rooted in DEMATEL's unique capability to explore causal patterns and provide decision-makers with a structured comprehension of the problem. Unlike conventional MCDM approaches, DEMATEL enables us to pinpoint the cause-and-effect associations among variables, therefore extracting meaningful insights into the fundamental origins of hidden connections and their ramifications on the overarching system.  
By visualizing and measuring these connections, DEMATEL can facilitate more discerning and effective decision-making processes. In contrast to alternative techniques, DEMATEL indeed holds a distinctive edge in its capacity to dissect latent connections within the system, and this capability proves invaluable in formulating well-informedand targeted strategies for enhancement. The primary methodological steps needed for employing DEMATEL are reported next [35].
* Gathering input data from experts regarding the cause-and-effect relationships among \(n\) factors, compared pairwise. These relationships are typically described using linguistic variables. The attributed qualitative descriptions of influence will be translated into numerical values using the following scale: 0 (No Influence, NO), 1 (Very Low Influence, VL), 2 (Low Influence, L), 3 (Medium Influence, M), 4 (High Influence, H), 5 (Very High Influence, VH). If multiple experts are involved in the data collection process, each expert should generate a squared \(n\times n\) matrix. These matrices should then be combined into a single squared input matrix (referred to as the direct-relation matrix \(A\)) before proceeding to the next phase.
* Normalizing the direct-relation matrix, achieving matrix \(D=s\times A\). This normalization is performed by computing the value \(s\), as follows: \[s=min\Bigg{[}\frac{1}{max_{1\leq i\leq n}\sum_{j=1}^{n}a_{ij}},\frac{1}{max_{1 \leq j\leq n}\sum_{i=1}^{n}a_{ij}}\Bigg{]}\] (1)
* Obtaining the total relation matrix \(T\). Such a calculation will take into account the identity matrix \(I\). In particular, it will involve the multiplication between matrix \(D\) and the inverse of the difference \(I-D\), activating an iteration process for which the generated matrix \(T\) will include direct and indirect effects related to the dataset under analysis: \[T=D\times(I-D)^{-1}.\] (2)
* Generating the causal relation map by analyzing the values within matrix \(T\) and establishing the most influential elements to be differentiated based on their prominence and relation values. Prominence and relation values are computed, respectively, as \(r_{i}+c_{i}\) and \(r_{i}-c_{i}\), where \(r_{i}\) and \(c_{i}\) are \(n\times 1\) and \(1\times n\) vectors, denoting the sum of rows and columns of matrix \(T\). In the causal relationship map, factors exhibiting higher prominence values are those with the greatest impact on the problem being examined. Moreover, factors with positive relationship values are deemed net contributors, while those with negative relationships are seen as net recipients [36]. The causal relationship map functions as a visual aid to scrutinize and depict the causal connections among the factors, facilitating a clear differentiation between the most influential and significant elements.
* Calculating the final vector of criteria weights by normalizing the corresponding prominence values.