Solving multicriteria problems of rating alternatives based on pairwise comparisons

  • Nikolai Krivulin Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia
  • Daria Bulgakova Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia
  • Dmitriy Grigoriev Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia
  • Karina Nagumanova Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia
  • Alexey Prinkov Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia
  • Yana Salova Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia
  • Arina Filatova Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia
Keywords: multicriteria decision making problems, pairwise comparisons, analytic hierarchy process, tropical mathematics

Abstract

Well-known examples of multicriteria problems of evaluating alternatives based on paired comparisons are considered. Numerical solutions to these problems are presented, obtained using the method of analytic hierarchy process, the method of weighted geometric means, and also a method based on the log-Chebyshev approximation of pairwise comparison matrices. When solving problems using log-Chebyshev approximation, models and methods of tropical mathematics are used, which studies the theory and applications of algebraic systems with idempotent operations.

Author Biographies

Nikolai Krivulin, Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia

Doctor of Sciences (Phys.-Math.), Professor, the Faculty of Mathematics and Mechanics, SPbGU, nkk@math.spbu.ru

Daria Bulgakova, Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia

student

Dmitriy Grigoriev, Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia

student

Karina Nagumanova, Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia

student

Alexey Prinkov, Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia

PhD student

Yana Salova, Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia

student

Arina Filatova, Saint Petersburg State University, 7–9, Universitetskaya emb., 198504, Saint Petersburg, Starii Petergof, Russia

student

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Published
2024-08-29
How to Cite
Krivulin, N., Bulgakova, D., Grigoriev, D., Nagumanova, K., Prinkov, A., Salova, Y., & Filatova, A. (2024). Solving multicriteria problems of rating alternatives based on pairwise comparisons. Computer Tools in Education, (2), 5-29. https://doi.org/10.32603/2071-2340-2024-2-5-29
Section
Algorithmic mathematics and mathematical modelling