## 4 Conclusions  
As a result of the study, the criteria for the evaluation system of XAI methods were determined. For a comprehensive assessment, it is necessary to take into account both the technical characteristics of the method, which can be determined experimentally or mathematically, and the sociological and cognitive characteristics that can be obtained in the course of sociological research and are strongly influenced by sampling parameters. At the same time, a balance should be observed between the types of metrics in order to eliminate the bias of the assessment.  
The considered analogues [7; 8; 9; 10; 11] with methodological and mathematical descriptions of metrics assumed the use of either technical or cognitive characteristics. In analogue [11], the importance of their joint use in the assessment was mentioned, but specific metrics were not indicated.  
From the study, the following conclusions can be drawn:  
Figure 5: The dependence of the monotonicity metric on the correlation coefficient.  
Figure 6: The incompleteness metric.  
* SHAP and LIME methods are comparable in terms of accuracy of explanation.A study was conducted, using these metrics, which determined the degradation in the explanation quality of the SHAP and LIME methods with increasing correlation in the input data;
* The completeness of explanations of both methods is satisfactory, but the weights of each feature separately, as well as the order of increasing weights, largely depend on the input data and the machine learning model;
* Both methods provide less accurate explanations as the correlation coefficient of features in the input data increases, with a correlation of >0.5, the explanations of the methods are unstable and may be questioned;
* Both methods provide less accurate explanations when applied to decision tree models than when applied to linear regression models;
* The SHAP method shows comparable explanatory accuracy with a linear and non-linear marker function, while the LIME method is less accurate with a non-linear function;
* The execution time of the LIME method is more than 10 times the execution time of the SHAP method.  
Further research on the basis of the developed tool for calculating metrics for evaluating the methods of explainable artificial intelligence can be aimed at:  
* Expansion of the list of XAI methods, for example, methods MAPLE, ER-SHAP, Breakdown;
* Study of evaluation metrics of XAI methods when applied to classification models;
* Study of dependence of SHAP method evaluation metrics on kernel parameters;
* Expansion of the list of machine learning models, for example, models of autoencoder, deep neural network, vector machines, convolutional neural network.  
Conceptualization, A.O. and N.S.; methodology, A.O.; software, A.O.; validation, N.S. and A.O.; writing--review and editing, N.S. and A.K.; project administration, A.K. and M.R. and A.D. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data Availability Statement: Data available in a publicly accessible repository. The data presented in this study are openly available at [[https://github.com/the21](https://github.com/the21) composer/XAI-Metric-Evaluator]([https://github.com/the21](https://github.com/the21) composer/XAI-Metric-Evaluator).  
Authors thank International Alexander Popov's Innovation Institute for Artificial Intelligence, Cybersecurity and Communications of Saint Petersburg Electrotechnical University \"LETI\" for support in work and research.  
The authors declare no conflict of interest.