## 4 Case Study
### Validation  
When assessing the code's functionality, it is necessary to look closely at the underlying algorithm. As widely explained throughout this paper, the system acts as a tool for processing and analyzing data, eventually leading to the generation of recommendations based on specific criteria. Built on the FCM framework, the proposed algorithm includes converting input data into fuzzy numbers, defuzzifying these numbers, calculating indirect and total effects, ranking elements according to their total effects, and ultimately prioritizing recommendations addressing those factors characterized by higher TE values. Furthermore, the code employs a network of relationships to enhance the traditional representation of results. The validation process has been led with a clear focus on examining the algorithm's logical and mathematical integrity, ensuring that it aligns with the intended analytical purpose. In practical terms, this means verifying its robustness across input matrices of diverse sizes, assessing its consistency in treating different datasets, and understanding how it responds to atypical scenarios and changes in the data. In the context of validation, defining suitable metrics tailored to the specific problem domain is essential, enabling us to measure the quality of recommendations effectively. We now validate the procedure, showing graphical results obtained by changing the input matrix containing linguistic evaluations expressed by experts. As a first input matrix, we use a larger matrix containing risk factors coming from the case study developed in previous research [4]. To run the system, it will be simply necessary to update the input data. The results are confirmed to be the same as reported in [4]. Figure 4 shows the network produced for this matrix, where we can clearly distinguish five different layers, each associated with different TE values, in a decreasing way. The obtained network represents a substantial advancement concerning the one reported in [4]. We want to stress further as elements with the associated highest TE occupy the first layers and, in some cases, as shown in Figure 4, the intensity of blue arrows can be lower for these elements. This can occur because an element's TE considers not only its direct connections but also the indirect ones through other elements in the map. Therefore, an element might have a high TE due to a web of indirect influences, even if its connections with certain elements are relatively weak. Essentially, when we consider the combined effect of numerous elements that may be indirectly linked, it becomes evident that their collective influence can result in a substantial TE, even if the individual relationships between these elements seem relatively weaker or less influential on their own. To further strengthen the validation of our recommendation system, we now proceed by iterating the procedure by using another input matrix available in the literature. In detail, we use data coming from a study led by [PERSON] et al. [56], which pertains to the mining sector, a high-risk environment that is distinct from airport infrastructure. This is to further corroborate the flexibility of our approach in dealing with different operational contexts. The mining sector poses substantial occupational risks spanning from the potential for accidents, environmental concerns, and the remote, challenging locations where mining activities take place. In carrying out the validation procedure, we used input data (collected by the authors in Table 8 [5]) and weighted TE values using their proposed approach (see weights reported in Table 9 [5]). We observe that the results are identical in terms of prioritization and, in our graphical representation (Figure 5), factors are automatically organized through layers according to the similarity exhibited in the ranking of factors reported by the authors (see Table 9 [5]). Our solution confirms that all the analyzed factors significantly affect the decision system of mining strategies.