## 2 Materials and Methods
### GERT Model for User Data Processing in the Recommendation System
#### 2.2.2 GERT Model of the Stage for Assigning Quantitative Weights to Identified Categories  
After completing the stage of initial categorization of the user request, the system proceeds to assign quantitative weights to each of the identified categories. This process is essential for determining the prioritization of various aspects of the request during the subsequent response generation. The second stage includes a sequence of operations organized according to the logic presented in Figure 5 as a GERT scheme. In the scheme presented in Figure 2, the arcs between nodes formalize the following state-to-state transitions. The arc \(W_{12}\) characterizes the start of the weight assignment process, the transition from the initial state to category analysis. The arc \(W_{23}\) illustrates the transition to verifying the correctness of the assigned weights. The arc \(W_{34}\) characterizes the transition to the weight correction procedure in case of an error. Accordingly, arc \(W_{42}\) illustrates the return to weight reassignment in case of an error. The transition and arc \(W_{35}\) characterize successful validation, after which two outcomes are possible. The first is the completion of the stage, the second is the clarification-based reassignment of weights. The second option is characterized by arc \(W_{52}\). Introducing the additional loop \(W_{52}\) increases the model's accuracy, bringing it closer to real-world scenarios, where even after the formal completion of a stage, returning to previous steps may occur due to changes in the request context, new requirements from the system or user, and inconsistencies between the assigned weights and current processing policies. This is especially relevant in adaptive or learning systems, where weight coefficients may be sensitive to the dynamics of input data. Taking into account the presented characteristics of the transitions in the GERT network for the stage of establishing quantitative importance weights for each identified category, the equivalent transfer function of the scheme (Figure 2) takes the following form:  
\[W_{E}(s)=W_{12}(s)W_{23}(s)\frac{W_{35}(s)}{1-W_{34}(s)W_{42}(s)W_{23}(s)-W_{ 52}(s)W_{23}(s)} \tag{17}\]  
The conducted analysis of the process formalized in Figure 5 made it possible to establish the characteristics of the branches considered in the GERT model and the distribution parameters. These are presented in more detail in Table 5. \begin{table}
\begin{tabular}{c c c} \hline
**Node** & **Stage** & **Purpose** \\ \hline
1 & Receiving categorized data & Initial stage; loading results from the previous step \\
2 & Assigning weights to data categories & Assigning quantitative importance values to each category \\
3 & Validating assigned weights & Checking the correctness and validity of weights \\
4 & Reassigning weights & Correcting weights if errors are detected \\
5 & Preparing the final formalized query & Final step: creating a unified structure for further request processing \\ \hline \end{tabular}
\end{table} 
Table 4: Description of the nodes and functions of the second stage GERT network (weight assignment module). Figure 5: GERT Scheme of the stage for assigning quantitative weights to identified categories. For each branch of the GERT network of the second stage, types of time distributions were selected that reflect the specifics of the corresponding operations. The basis for this selection is the structure of the algorithm itself, the type of transition, and the nature of processing inherent to each stage. In particular, the most complex and logically intensive processes--weight assignment \(W_{12}\) and its validation \(W_{23}\)--are modeled using an Erlang distribution of order \(k=2\), reflecting the two-phase nature of these steps. This makes it possible to account for delays caused by the need to go through a series of logical checks or calculations.