## 5 The IDEMATEL Algorithm
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Criteria** & **FO** & **UA** & **SI** & **QS** & **CV** & **SC** & **RR** \\ \hline FO & 0.615483 & 0.700611 & 0.700611 & 0.809385 & 0.777539 & 0.672040 & 0.868314 \\ UA & 0.586781 & 0.429056 & 0.524294 & 0.617193 & 0.552236 & 0.529353 & 0.664188 \\ SI & 0.592153 & 0.529982 & 0.434743 & 0.582269 & 0.558179 & 0.536459 & 0.743810 \\ QS & 0.710256 & 0.653214 & 0.653214 & 0.580363 & 0.687035 & 0.634654 & 0.794699 \\ CV & 0.730663 & 0.624210 & 0.624210 & 0.728502 & 0.563766 & 0.715220 & 0.838054 \\ SC & 0.456101 & 0.467019 & 0.467019 & 0.509966 & 0.488738 & 0.380419 & 0.651403 \\ RR & 0.493836 & 0.463589 & 0.463589 & 0.508177 & 0.487105 & 0.470331 & 0.480049 \\ \hline \end{tabular}
\end{table} 
Table 7: Total influence matrix \(\mathbf{T}\) showing the cumulative effects among criteria for GenAI tool selection. This table summarizes the influence and dependency of each criterion in the selection of GenAI tools, highlighting their relative importance and causal relationships. The weights reflect the criteria's overall impact on decision-making, guiding prioritization in academic research tool evaluation. A comparison of the IDEMATEL results with DEMATEL method and the Revised DEMATEL results obtained by [PERSON] is presented in Table 9. Because the maximum sum of the rows in matrix **D** (19) equals the maximum sum of the columns (19), the Revised DEMATEL method proposed by [PERSON] uses \(\varepsilon\) = 0.001 to calculate the normalized initial direct-relation matrix \(\overline{\textbf{D}}\). In this case, the matrix \(\overline{\textbf{D}}\) from [PERSON]'s method is not equal to the matrix \(\overline{\textbf{D}}\) from the original DEMATEL method. The results obtained using the IDEMATEL method are identical to those from the DEMATEL method, with the important distinction that IDEMATEL guarantees the convergence condition, allowing the total influence matrix **T** to be computed for any normalized initial direct-relation matrix \(\overline{\textbf{D}}\). By mapping the vectors \(\textbf{r}^{\star}\) and \(\textbf{r}^{-}\) the data are displayed in a causality diagram (Figure 2). The causality diagram visualizes the causal relationships among the criteria. A causality diagram (Figure 2) visually represents the causal relationships among criteria. This type of diagram helps to illustrate which criteria act as causes (influencers) and which as effects (influenced), making complex interdependencies easier to interpret and analyze. In the context of selecting a GenAI tool for academic research, the results obtained from the IDEMATEL method reveal how different criteria influence each other. Driving (cause) criteria are \"Functionality and Objectives\" (\(\textbf{r}^{-}\) = 0.958), \"Cost and Value\" (\(\textbf{r}^{-}\) = 0.710) and \"Data Quality and Security\" (\(\textbf{r}^{-}\) = 0.377). \"Functionality and Objectives\" represents the core capabilities of a GenAI tool, such as generating text, performing data analysis, or assisting with literature reviews. This criterion is important because it defines the primary purpose and use cases the GenAI can support in academic research. GenAI tools like ChatGPT 4, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Criteria Symbols** & **Criteria** & **a** & **b** & \(\textbf{r}^{\star}\) & \(\textbf{r}^{-}\) & \(\textbf{r}^{+}\) & **w** \\ \hline FO & Functionality and Objectives & 5.14398 & 4.18527 & 9.32926 & 0.95871 & 1 & 0.15893 \\ UA & Ease of Use and Accessibility & 3.90310 & 3.86768 & 7.77078 & 0.03542 & 6 & 0.13238 \\ SI & Scalability and Integration & 3.97760 & 3.86768 & 7.84528 & 0.10991 & 5 & 0.13365 \\ QS & Data Quality and Security & 4.71343 & 4.33586 & 9.04929 & 0.37758 & 2 & 0.15416 \\ CV & Cost and Value & 4.82463 & 4.11460 & 8.93922 & 0.71003 & 3 & 0.15229 \\ SC & Support and Community & 3.42067 & 3.93847 & 7.35914 & \(-\)0.51781 & 7 & 0.12537 \\ RR & Reputation and Reviews & 3.36667 & 5.04052 & 8.40719 & \(-\)1.67384 & 4 & 0.14322 \\ \hline \hline \end{tabular}
\end{table}