Feedback loop scheme as related to axiomatic approach to Pareto set reduction

Authors

  • Alexander V. Sachkov St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

DOI:

https://doi.org/10.21638/spbu10.2024.212

Abstract

A feedback loop scheme is proposed as related to axiomatic approach to Pareto set reduction. Necessary information on axiomatic approach is presented and an example is studied. The feedback loop scheme is explored as related to a problem of potential insurance contract conclusion. Problems arising with such approach are discussed, such as criteria selection, automatic quanta collection based on user behavior data and others. The scheme is then modified and an approximate solution algorithm is presented. Future research directions are outlined.

Keywords:

choice, Pareto set, feedback loop

Downloads

Download data is not yet available.
 

References

Литература

Hamel A. H., Kostner D. Multi-weight ranking for multi-criteria decision making // arXiv: 2312.03006. URL: https://arxiv.org/abs/2312.03006 (дата обращения: 2 декабря 2023 г.).

Bednarczuk E. M., Miroforidis Ja., Przemyslaw Pz. A multi-criteria approach to approximate solution of multiple-choice knapsack problem // arXiv: 1712.06723. URL: https://arxiv.org/abs/1712.06723 (дата обращения: 2 декабря 2023 г.).

Ногин В. Д. Сужение множества Парето: аксиоматический подход. М.: Физматлит, 2018. 272 с.

Басков О. В. Алгоритм последовательного учета информации об относительной важности критериев в задаче многокритериального выбора // Процессы управления и устойчивость: Труды 41-й междунар. конференции аспирантов и студентов / под ред. Н. В. Смирнова, Г. Ш. Тамасяна. СПб.: Издат. дом Санкт-Петербургского университета, 2010. С. 553–558.

Erdil E., Besiroglu T. Explosive growth from AI automation: A review of the arguments // arXiv: 2309.11690. URL: https://arxiv.org/abs/2309.11690 (дата обращения: 2 декабря 2023 г.).

Сачков А. В. Исследование возможности заключения договора страхования с учетом функции полезности // Вестник Санкт-Петербургского университета. Прикладная математика. Информатика. Процессы управления. 2023. Т. 19. Вып. 3. С. 369–373. https://doi.org/10.21638/11701/spbu10.2023.305

Duan R., Wu H., Zhou R. Faster matrix multiplication via asymmetric hashing // arXiv: 2210.10173. URL: https://arxiv.org/abs/2210.10173 (дата обращения: 2 декабря 2023 г.).

Ilyushina A. N., Pershin I. M., Trushnikov V. E., Novozhilov I. M., Pervukhin D. A., Tukeyev D. L. Design of a software complex for control of induction equipment of metallurgical manufacture using systems theory // 2023 V International Conference on Control in Technical Systems (CTS). St. Petersburg: LETI Publ., 2023. P. 83–87.

Novozhilov I. M., Sidorenko A. A., Tukeyev D. L., Podkina M. E., Pervukhin D. A., Trushnikov V. E. Design of software and hardware complex of temperature field diagnostics using the theory of distributed parameter systems // 2023 V International Conference on Control in Technical Systems (CTS). St. Petersburg: LETI Publ., 2023. P. 88–91.


References

Hamel A. H., Kostner D. Multi-weight ranking for multi-criteria decision making. arXiv: 2312.03006. Available at: https://arxiv.org/abs/2312.03006 (accessed: December 2, 2023).

Bednarczuk E. M., Miroforidis Ja., Przemyslaw Pz. A multi-criteria approach to approximate solution of multiple-choice knapsack problem. arXiv: 1712.06723. Available at: https://arxiv.org/abs/1712.06723 (accessed: December 2, 2023).

Noghin V. D. Reduction of the Pareto set: an axiomatic approach. Cham, Switzerland, Springer, 2014, XIX, 232 p. (Rus. ed.: Nogin V. D. Suzhenie mnozhestva Pareto: aksiomaticheskii podkhod. Moscow, Physmatlit Publ., 2018. 272 p.)

Baskov O. V. Algoritm posledovatel'nogo ucheta informatsii ob otnositel'noi vazhnosti kriteriev v zadache mnogokriterial'nogo vybora [Algorithm for sequential accounting of information on the relative criteria importance in the multicriteria choice problem]. The XLI Annual International Conference on Control Processes and Stability (CPS'10). St. Petersburg, Publishing House of St. Petersburg State University, 2010, pp. 553–558. (In Russian)

Erdil E., Besiroglu T. Explosive growth from AI automation: A review of the arguments. arXiv: 2309.11690. Available at: https://arxiv.org/abs/2309.11690 (accessed: December 2, 2023).

Sachkov A. V. Issledovanie vozmozhnosti zakliucheniia dogovora strakhovaniia s uchetom funktsii poleznosti [Examining the possibility of insurance contract conclusion based on utility function]. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Sciences. Control Processes, 2023, vol. 19, iss. 3, pp. 369–373. https://doi.org/10.21638/11701/spbu10.2023.305 (In Russian)

Duan R., Wu H., Zhou R. Faster matrix multiplication via asymmetric hashing. arXiv: 2210.10173. Available at: https://arxiv.org/abs/2210.10173 (accessed: December 2, 2023).

Ilyushina A. N., Pershin I. M., Trushnikov V. E., Novozhilov I. M., Pervukhin D. A., Tukeyev D. L. Design of a software complex for control of induction equipment of metallurgical manufacture using systems theory. 2023 V International Conference on Control in Technical Systems (CTS). St. Petersburg, LETI Publ., 2023, pp. 83–87.

Novozhilov I. M., Sidorenko A. A., Tukeyev D. L., Podkina M. E., Pervukhin D. A., Trushnikov V. E. Design of software and hardware complex of temperature field diagnostics using the theory of distributed parameter systems. 2023 V International Conference on Control in Technical Systems (CTS). St. Petersburg, LETI Publ., 2023, pp. 88–91.

Published

2024-07-08

How to Cite

Sachkov, A. V. (2024). Feedback loop scheme as related to axiomatic approach to Pareto set reduction. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 20(2), 281–288. https://doi.org/10.21638/spbu10.2024.212

Issue

Section

Control Processes