004.9

VIKOR, information technology, MCDM, intuitionistic fuzzy sets, analytic hierarchy process.

The model for supporting the student decision in choosing the subjects of specialty educational program based on VIKOR multi-criteria optimization method is developed in this paper. The developed model is the component of the dual education information system (when the student is trained in the company and educational institution at the same time on the basis of the contract). This component is a decision support tool for a student training by a dual education, taking into account the expert opinion of stakeholders in the learning process. The criteria of dual education stakeholders for ranking alternatives (subjects of the specialty program): student, educational institution, company are outlined. VIKOR method is modified by the selection of subsystems criteria in order to derive an integrated assessment of experts from different subsystems. The algorithm for integrating ratings of ranking subsystems is developed, taking into account the strategy of maximum group usefulness of VIKOR method. The weighting coefficients of subsystems and their criteria are determined by T. Saati method of hierarchies analysis. In order to take into account the uncertainty associated with the lack of information, intuitionistic fuzzy sets are used to assign assessments of the alternatives ranking by subsystem experts. The proposed modification of VIKOR method makes it possible to rank the alternatives with the involvement of different specialists with their own criteria system. This approach increases the accuracy of the obtained results, as the criteria are further divided into holders subsystems of the ranking problem. This approach enables to carry out deeper and broader analysis of ranking problem aspects. Numerical example of the developed model which confirms the acceptability of its application in practice in the dual educational process application is illustrated in this paper.

1. Habib, M. N., Jamal, W., Khalil, U., & Khan, Z. Transforming universities in interactive digital platform: case of city university of science and information technology. Education and Information Technologies. 26 (1). 2021. Р. 517–541.
2. Ifenthaler, D. (Ed.). Digital workplace learning: Bridging formal and informal learning with digital technologies. Springer. 2018.
3. Latchem, C. Using ICTs and blended learning in transforming technical and vocational education and training. UNESCO Publishing. 2017.
4. Hwang, C. L., & Yoon, K.. Methods for multiple attribute decision making. In Multiple attribute decision making. 1981. P. 58–191. Springer, Berlin, Heidelberg.
5. Opricovic, S., & Tzeng, G. H.. Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European journal of operational research. 156 (2). 2004. Р. 445–455.
6. Keshavarz Ghorabaee, M., Zavadskas, E. K., Turskis, Z., & Antucheviciene, J. A new combinative distance-based assessment (CODAS) method for multi-criteria decision-making. Economic Computation & Economic Cybernetics Studies & Research. 50 (3). 2016.
7. Gomes, L. F. A. M., & Lima, M. M. P. P.. TODIM: Basics and application to multicriteria ranking of projects with environmental impacts. Foundations of computing and decision sciences. 16 (4). 1992. Р. 113–127.
8. Gomes, L. F. A. M., & Lima, M. M. P. P.. From modeling individual preferences to multicriteria ranking of discrete alternatives: a look at prospect theory and the additive difference model. Foundations of Computing and Decision Sciences. 17 (3). 1992. Р. 171–184.
9. Figueira, J. R., Mousseau, V., & Roy, B.. ELECTRE methods. In Multiple criteria decision analysis. Springer, New York. NY. 2016. Р. 155–185.
10. Brans, J. P., & Mareschal, B. The PROMETHEE methods for MCDM; the PROMCALC, GAIA and BANKADVISER software. In Readings in multiple criteria decision aid. 1990. P. 216–252, Springer, Berlin, Heidelberg.
11. Gul, M., Celik, E., Aydin, N., Gumus, A. T., & Guneri, A. F.. A state of the art literature review of VIKOR and its fuzzy extensions on applications. Applied Soft Computing. 46. 2016. Р. 60–89.
12. Lin, M., Chen, Z., Xu, Z., Gou, X., & Herrera, F. Score function based on concentration degree for probabilistic linguistic term sets: an application to TOPSIS and VIKOR. Information Sciences. 551. 2021. Р. 270–290.
13. Gou, X., Xu, Z., Liao, H., & Herrera, F. Probabilistic double hierarchy linguistic term set and its use in designing an improved VIKOR method: The application in smart healthcare. Journal of the Operational Research Society. 2020. 1–20.
14. Li, H., Wang, W., Fan, L., Li, Q., & Chen, X. A novel hybrid MCDM model for machine tool selection using fuzzy DEMATEL, entropy weighting and later defuzzification VIKOR. Applied Soft Computing. 91. Р. 106–207. 2020.
15. Sanayei, A., Mousavi, S. F., & Yazdankhah, A. Group decision making process for supplier selection with VIKOR under fuzzy environment. Expert Systems with Applications. 37 (1. 2010. Р. 24–30.
16. Ju, Y., & Wang, A. Extension of VIKOR method for multi-criteria group decision making problem with linguistic information. Applied Mathematical Modelling. 37 (5). 2013. Р. 3112–3125.
17. Atanassov, K. T. Intuitionistic Fuzzy Sets: Theory and Applications. Vol. 35. 1999. Studies in Fuzziness and Soft Computing.
18. Rouyendegh, B. D. The intuitionistic fuzzy ELECTRE model. International Journal of Management Science and Engineering Management. 13 (2). 2018. Р. 139–145.
19. Onat, N. C., Gumus, S., Kucukvar, M., & Tatari, O.. Application of the TOPSIS and intuitionistic fuzzy set approaches for ranking the life cycle sustainability performance of alternative vehicle technologies. Sustainable Production and Consumption. 6. 2016. Р. 12–25.
20. Saaty, T. L. A scaling method for priorities in hierarchical structures. Journal of mathematical psychology. 15 (3). 1977. Р. 234–281.

1. Habib, M. N., Jamal, W., Khalil, U., & Khan, Z. Transforming universities in interactive digital platform: case of city university of science and information technology. Education and Information Technologies. 26 (1). 2021. Р. 517–541.
2. Ifenthaler, D. (Ed.). Digital workplace learning: Bridging formal and informal learning with digital technologies. Springer. 2018.
3. Latchem, C. Using ICTs and blended learning in transforming technical and vocational education and training. UNESCO Publishing. 2017.
4. Hwang, C. L., & Yoon, K.. Methods for multiple attribute decision making. In Multiple attribute decision making. 1981. P. 58–191. Springer, Berlin, Heidelberg.
5. Opricovic, S., & Tzeng, G. H.. Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European journal of operational research. 156 (2). 2004. Р. 445–455.
6. Keshavarz Ghorabaee, M., Zavadskas, E. K., Turskis, Z., & Antucheviciene, J. A new combinative distance-based assessment (CODAS) method for multi-criteria decision-making. Economic Computation & Economic Cybernetics Studies & Research. 50 (3). 2016.
7. Gomes, L. F. A. M., & Lima, M. M. P. P.. TODIM: Basics and application to multicriteria ranking of projects with environmental impacts. Foundations of computing and decision sciences. 16 (4). 1992. Р. 113–127.
8. Gomes, L. F. A. M., & Lima, M. M. P. P.. From modeling individual preferences to multicriteria ranking of discrete alternatives: a look at prospect theory and the additive difference model. Foundations of Computing and Decision Sciences. 17 (3). 1992. Р. 171–184.
9. Figueira, J. R., Mousseau, V., & Roy, B.. ELECTRE methods. In Multiple criteria decision analysis. Springer, New York. NY. 2016. Р. 155–185.
10. Brans, J. P., & Mareschal, B. The PROMETHEE methods for MCDM; the PROMCALC, GAIA and BANKADVISER software. In Readings in multiple criteria decision aid. 1990. P. 216–252, Springer, Berlin, Heidelberg.
11. Gul, M., Celik, E., Aydin, N., Gumus, A. T., & Guneri, A. F.. A state of the art literature review of VIKOR and its fuzzy extensions on applications. Applied Soft Computing. 46. 2016. Р. 60–89.
12. Lin, M., Chen, Z., Xu, Z., Gou, X., & Herrera, F. Score function based on concentration degree for probabilistic linguistic term sets: an application to TOPSIS and VIKOR. Information Sciences. 551. 2021. Р. 270–290.
13. Gou, X., Xu, Z., Liao, H., & Herrera, F. Probabilistic double hierarchy linguistic term set and its use in designing an improved VIKOR method: The application in smart healthcare. Journal of the Operational Research Society. 2020. 1–20.
14. Li, H., Wang, W., Fan, L., Li, Q., & Chen, X. A novel hybrid MCDM model for machine tool selection using fuzzy DEMATEL, entropy weighting and later defuzzification VIKOR. Applied Soft Computing. 91. Р. 106–207. 2020.
15. Sanayei, A., Mousavi, S. F., & Yazdankhah, A. Group decision making process for supplier selection with VIKOR under fuzzy environment. Expert Systems with Applications. 37 (1. 2010. Р. 24–30.
16. Ju, Y., & Wang, A. Extension of VIKOR method for multi-criteria group decision making problem with linguistic information. Applied Mathematical Modelling. 37 (5). 2013. Р. 3112–3125.
17. Atanassov, K. T. Intuitionistic Fuzzy Sets: Theory and Applications. Vol. 35. 1999. Studies in Fuzziness and Soft Computing.
18. Rouyendegh, B. D. The intuitionistic fuzzy ELECTRE model. International Journal of Management Science and Engineering Management. 13 (2). 2018. Р. 139–145.
19. Onat, N. C., Gumus, S., Kucukvar, M., & Tatari, O.. Application of the TOPSIS and intuitionistic fuzzy set approaches for ranking the life cycle sustainability performance of alternative vehicle technologies. Sustainable Production and Consumption. 6. 2016. Р. 12–25.
20. Saaty, T. L. A scaling method for priorities in hierarchical structures. Journal of mathematical psychology. 15 (3). 1977. Р. 234–281.