## 5 The IDEMATEL Algorithm
\tag{13}\]  
The resulting binary matrix \(\mathbf{G}\) is then used for constructing the IRM and digraph. _Arithmetic Mean--Standard Deviation (MSD) Method_  
This method refines the threshold by incorporating both the arithmetic mean \(\mu\) and the standard deviation \(\sigma\) of matrix \(\mathbf{T}\). The threshold is calculated as \(\theta=\mu+\sigma\). The resulting matrix is then used for IRM construction and digraph design. The algorithm is also presented in Figure 1. Figure 1 illustrates the step-by-step process of the IDMATEL method, including the construction of the initial direct-relation matrix, normalization, calculation of the total influence matrix, and derivation of the cause-effect relationships among criteria. The algorithm ensures convergence and provides a comprehensive framework for analyzing interdependencies in multi-criteria decision-making problems. Figure 1: Flowchart of the IDEMATEL algorithm. An Application of the IDEMATEL Method for Evaluation and Analysis of Criteria Used in Selection of GenAI Tools for Academic Research  
The framework based on the IDEMATEL method is applied to analyze cause-and-effect relationships among a set of criteria for the selection of a suitable GenAI tool for academic research. A group of three experts, with solid knowledge and experience in the field was chosen. These experts select a set of important criteria for GenAI tools, based on their experience and a review of the literature. The criteria selected are Functionality and Objectives, Ease of Use and Accessibility, Scalability and Integration, Data Quality and Security, Cost and Value, Support and Community and Reputation and Reviews (Table 4). The criteria are interconnected, with some having a direct influence on others (e.g., functionality depending on data quality). The importance of each criterion can vary depending on the specific research context (e.g., data quality is paramount for systematic reviews). Using the IDEMATEL scale, each expert performed evaluations of each criterion in relation to all other criteria. The \(\mathbf{D}^{(k)}\) (initial direct-relation matrix for each expert \(k\)) is built. Then, based on Equation (1), the matrix \(\mathbf{D}\) is obtained (Table 5). Each cell (_i,j_) shows the direct influence of criterion \(i\) on criterion \(j\), scored by experts using the IDEMATEL scale. The diagonal values are zero since a criterion does not in \begin{table}
\begin{tabular}{c c c} \hline \hline
**Criterion** & **Symbol** & **Description** \\ \hline Functionality and Objectives & FO & Alignment of the tool’s features with specific research tasks (literature review, data analysis, writing, etc.). \\ \hline Ease of Use and Accessibility & UA & User-friendliness for researchers with varying technical expertise; intuitive interfaces; compatibility across platforms. \\ \hline Scalability and Integration & SI & The tool’s ability to handle increasing data/demands and integrate with existing research workflows and systems. \\ \hline Data Quality and Security & QS & Ensuring data accuracy, reliability, and protection against breaches; maintaining privacy. \\ \hline Cost and Value & CV & Balancing the cost (subscriptions, usage charges) with the value provided (efficiency, accuracy, improved outcomes). \\ \hline Support and Community & SC & Availability of technical support, training resources, and a community of users for assistance and best practices. \\ \hline Reputation and Reviews & RR & Overall reputation of the AI tool and vendor; feedback from other users. \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Key criteria for selecting GenAI tools in academic research, including their symbols and detailed descriptions.