## 3 Results
### Case Study of Sugeno Fuzzy Logic System  
The case study in this paper is based on the application of an approach founded on a developed Sugeno fuzzy logic system [51; 52]. The main goal is to assess the likelihood of the occurrence of a group of risks for a specific project under consideration. Subsequently, following the methodology, the probability of each individual risk within the groups can be assessed. Data from significant road infrastructure projects in the Republic of Serbia were used for training and testing the fuzzy logic system. For the purposes of the study, two FISs were developed in MATLAB 2024a, both with identical structures, as shown in Figure 2. They differ in that one pertains to the occurrence of major risk groups (FIS F1) and the other to secondary risk groups (FIS F2). They were trained with different datasets, using the same input variables but yielding distinct output values representing probabilities for major and secondary risk groups. The systems consist of three input (coefficients: K1-K3) and seven output (risk groups: RG1-RG7) variables. The obtained probability values for the risk groups at the output can be used, based on Equation (1), to determine the probability of each individual risk within the groups. In Figure 3, the input variables in fuzzy logic systems F1 and F2 are presented, along with their basic characteristics, degree of membership, and value ranges, as can be inferred from the figure. Gaussian functions were used to describe the input variables, while the seven output variables were modeled using linear functions. Gaussian membership functions provide continuous and smooth transitions between fuzzy sets, which is crucial for accurately modeling uncertainty in complex projects. Compared to other membership functions (e.g., triangular or trapezoidal), Gaussian functions are less sensitive to noise in the input data, making them more stable in real-world applications. Additionally, Gaussian functions are differentiable everywhere, facilitating the optimization and fine-tuning of fuzzy logic models, especially when combined with machine learning techniques. Linear output functions allow for faster computation compared to more complex nonlinear functions, making the model more practical for real-time applications. In a Sugeno-type system, using linear output functions simplifies the defuzzification process, ensuring that final risk probabilities are computed efficiently. As previously mentioned, two fuzzy logic systems were created, and for this purpose, two datasets were prepared for their training. The input parameters remain the same, while the outputs differ, as they pertain to the probabilities of risk group occurrences as major and secondary. As stated earlier, the available data originate from a dataset comprising 28 road infrastructure projects in the Republic of Serbia. With three projects set aside for testing, 25 fuzzy rules were generated based on the remaining 25 projects. It is important to emphasize that systems of this type can always be improved by expanding their training datasets, thereby increasing the number of rules and, consequently, enhancing the accuracy and reliability of output modeling during application. This adaptability makes them particularly useful in dynamic and complex environments, such as risk assessment in infrastructure projects. From Figure 3, it can be concluded that the membership functions for the input variable K1 are relatively evenly distributed, with overlaps that allow for smooth transitions between fuzzy sets. For the variable K2, a denser distribution of membership functions is noticeable in the central part of the domain, which may indicate higher precision in that segment. In the case of the variable K3, the domain is significantly wider compared to the previous variables, and the large number of membership functions with substantial overlap suggests a detailed segmentation of values. The testing of the developed systems was conducted using data from three real road infrastructure projects in the Republic of Serbia.