Researchers should consider criteria such as functionality, ease of use, cost, security, community support, and reputation that can have different levels of importance and can influence each other. These criteria can be used in a selection of GenAI tools based on a multi-criteria method. While various multi-criteria and weighting methods can be applied to evaluate, selection and adoption of GenAI tools, there is a lack of studies focused on GenAI tools for academic research that consider causal relationships between evaluation criteria. The Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is a method capable of modeling causal relationships among criteria for analysis of criteria used in selection of a GenAI tool for academic research [5]. It identifies cause-and-effect relationships between criteria, facilitating better prioritization and decision-making. By visualizing these relationships, DEMATEL helps decision-makers understand how criteria affect the decision process. Using a structured framework based on DEMATEL ensures that the selection process is systematic and accurate. The gap in analysis of causal relationships between evaluation criteria emphasizes the need for more sophisticated decision-support methods that model the influence and interaction between criteria. This paper aims to fill this gap by proposing an Improved Group DEMATEL method called IDEMATEL, that models the causal relationships between the criteria involved in the selection of GenAI tools for academic research. IDEMATEL offers a systematic approach to identify cause-and-effect relationships, with the advantage of ensuring that the successive powers of the initial direct relation matrix converge to zero, allowing for the computation of the total influence matrix. The paper provides theoretical foundations for evaluating whether the powers of a square matrix converge to zero using spectral radius and some matrix norms. The method constructs a causality diagram and digraph to visually represent the relationships among criteria. An application of the IDEMATEL method that involves the evaluation the criteria used to select a suitable GenAI tool for academic research: 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 are developed and analyzed. In summary, this paper provides  
1. A review of evaluation criteria relevant to the selection of GenAI tools for academic research. 2. A IDEMATEL method that enhances the classical DEMATEL approach. 3. An application of the IDEMATEL method to analyze interdependencies among criteria in selecting a GenAI tool for academic research. By providing both theoretical contributions and practical insights, this study aims to support researchers and institutions in making informed, structured, and justifiable decisions when selecting GenAI tools for academic use. The remainder of the paper is structured as follows. Section 2 presents recent research in the selection, adoption, and implementation of GenAI tools based on multi-criteria methods. A review of the criteria that should be considered when selecting GenAI tools for academic research is realized. Section 3 argues the reasons for selecting the DEMATEL method for evaluation and analysis of the criteria. The IDEMATEL method and the algorithm are proposed in Sections 4 and 5. An application of the proposed method for evaluation and analysis of criteria used in the selection of GenAI tools for academic research is presented in Section 6. Conclusions are given in Section 7.