## 5 The IDEMATEL Algorithm
Only criteria whose influence value in matrix **T** is higher than the threshold value can be chosen and converted into the IRM. The digraph for this threshold is illustrated in Figure 3.  
The digraph visualizes the significant causal relationships among the criteria for selecting GenAI tools in academic research. Each node represents a specific criterion, and each directed arrow (edge) indicates that one criterion has a direct influence on another, as determined by the threshold value (\(\mu=0.599\)). The arrows point from the influencing criterion (cause) to the influenced criterion (effect). Criteria with many outgoing arrows, such as \"Functionality and Objectives\" and \"Data Quality and Security\", act as key drivers  
Figure 3: The digraph for \(\mu=0.599\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Criterion** & **ChatGPT** & **Perplexity** & **Scite.ai (Scite (New York, NY, USA)** & **Gemini (Google** & **Claude (Anthropic)** \\ \hline Scalability and Integration & 4 (API for developers, plug-ins for various apps, API rate limits) & 4.3 (Collaboration features, Sonar API access) & 4.8 (Integrates with Zotero, EndNote, browser plug-ins) & 5 (Native integration with Google services) & 4.4 (API and enterprise workflow integration) \\ \hline Reputation and Reviews & 4.6 (Widely adopted, 100M+ users) & 4.8 (Speed, accuracy, and citation transparency) & 4.9 (Highly regarded citations analysis, context, and integration) & 4.7 (Recognized for multimodal process, trusted infrastructure, Google credibility) & 4.5 (High ethical standards, top-rated for safety) \\ \hline Support and Community & 4 (OpenAI forums, support channels, community for forums) & 4.5 (Priority support for Pro, active community) & 4.7 (Institution webinars, documentation, responsive support; growing reputation in academia) & 4.8 (Google Cloud support, large user base) & 4.6 (Dedicated enterprise support) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: _Cont._in the system. They influence multiple other criteria, suggesting that improvements or changes in these areas are likely to have a broad impact. Criteria with many incoming arrows, such as \"Reputation and Reviews\", are more dependent on other factors. Their status is shaped by changes in other criteria. This digraph helps to identify which criteria should be prioritized in decision-making, as influencing them can lead to widespread improvements across the system. The threshold value of 0.599 was selected based on the distribution of influence values in the total influence matrix. This value effectively filters out weaker, less significant relationships, allowing the digraph to highlight only the most meaningful and impactful connections between criteria. By using this threshold, the resulting digraph avoids excessive complexity and focuses the analysis on the dominant causal pathways, making the visualization more interpretable and actionable. We also tested other threshold values and found that 0.599 provides a balanced representation, neither omitting important relationships nor overcrowding the diagram with minor influences. The IDEMATEL method offers several key advantages over traditional approaches for analyzing criteria in the selection of GenAI tools. First and foremost, it enables a comprehensive mapping of both direct and indirect relationships among criteria, providing a holistic view of how improvements in one area can cascade through the system and affect others. This causality analysis allows decision-makers to identify not only the most influential criteria but also the pathways through which these criteria impact overall outcomes, supporting more strategic prioritization and resource allocation. A significant technical advantage of IDEMATEL is its robust approach to calculating the total influence matrix. Unlike classical DEMATEL methods, which may fail or produce unreliable results if certain mathematical conditions are not met, IDEMATEL introduces a generalized convergence condition.