A soft sets review
- Authors: Bobylevа V.N.1, Egorova E.K.1, Leonov V.Y.1
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Affiliations:
- Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences
- Issue: No 4 (2024)
- Pages: 148-153
- Section: ARTIFICIAL INTELLIGENCE
- URL: https://permmedjournal.ru/0002-3388/article/view/676404
- DOI: https://doi.org/10.31857/S0002338824040102
- EDN: https://elibrary.ru/UDWLOK
- ID: 676404
Cite item
Abstract
In this review we consider the so-called soft sets. In fact, it is a generalization of L. Zadeh’s fuzzy sets, which form the mathematical apparatus of artificial intelligence. On the other hand, the rejection of the notion of infinitesimality originates the foundations of a new mathematical analysis. Subsequently, many papers on soft sets have appeared, conferences have been organized, and there are publications on applications in various fields. The paper gives the basic definitions and terms of soft sets theory, and references to its practical applications.
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About the authors
V. N. Bobylevа
Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences
Author for correspondence.
Email: vbobylev@frccsc.ru
Russian Federation, Moscow
E. K. Egorova
Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences
Email: eegorova@frccsc.ru
Russian Federation, Moscow
V. Yu. Leonov
Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences
Email: vleonov@frccsc.ru
Russian Federation, Moscow
References
- Zadeh L.A. Fuzzy Sets // Inf. Control. 1965. V. 8. № 3. P. 338–353. ISSN 0019-9958. https://doi.org/10.1016/S0019-9958(65)90241-X.
- Molodtsov D.A. Soft Set Theory – First Results // Computers & Mathematics with Applications. 1999. V. 37. № 4/5. P. 19–31. ISSN 0898-1221, 1873-7668. https://doi.org/10.1016/s0898-1221(99)00056-5.
- Молодцов Д.А. Устойчивость и регуляризация принципов оптимальности // ЖВМиМФ. 1980. Т. 20. № 5. С. 25–38. ISSN 0041-5553. https://doi.org/10.1016/0041-5553(80)90086-5.
- Молодцов Д.А. Аппроксимация принципов оптимальности в задаче нахождения кратного максмина // Докл. АН СССР. 1985. Т. 32. С. 426–428. ISSN 0197-6788.
- Молодцов Д.А. Структура регуляризующих принципов оптимальности // Докл. АН СССР. 1985. Т. 32. С. 82—85. ISSN 0197-6788.
- Молодцов Д.А., Ковков Д.В. Устойчивость и аппроксимация максиминных задач // АиТ. 2014. Т. 75. № 3. С. 447–457. ISSN 0005-1179, 1608-3032. https://doi.org/ 10.1134/S0005117914030035.
- Молодцов Д.А. Принципы оптимальности как математическая модель поведения человека // Математическое моделирование. 1991. Т. 3. № 5. С. 29–48. ISSN 0234-0879.
- Ma Z.M., Yang W., Hu B.Q. Soft Set Theory Based on Its Extension // Fuzzy Information and Engineering. 2010. V. 2. № 4. P. 423–432. ISSN 1616-8658. https://doi.org/10.1007/s12543-010-0060-7.
- Maji P.K., Biswas R., Roy A.R. Soft Set Theory // Computers & Mathematics with Applications. 2003. V. 45. № 4. P. 555–562. ISSN 0898-1221. https://doi.org/10.1016/S0898-1221(03)00016-6.
- Ali M.I., Feng F., Liu X., Min W.K., Shabir M. On Some New Operations in Soft Set Theory // Computers & Mathematics with Applications. 2009. V. 57. № 9. P. 1547–1553. ISSN 0898-1221, 1873-7668. https://doi.org/10.1016/j.camwa.2008.11.009.
- Yang C.F. A Note on “Soft Set Theory” [Comput. Math. Appl. 45 (4–5) (2003) 555–562] // Computers & Mathematics with Applications. 2008. V. 56. № 7. P. 1899–1900. ISSN 0898-1221. https://doi.org/10.1016/j.camwa.2008.03.019.
- Молодцов Д.А. Структура мягких множеств // Нечеткие системы и мягкие вычисления. 2017. Т. 12. № 1. С. 5–18. ISSN 1819-4362.
- Kovkov D.V., Kolbanov V.M., Molodtsov D.A. Soft Sets Theory-based Optimization // J. Computer and Systems Sciences International. 2007. V. 46. № 6. P. 872–880. ISSN 1064-2307, 1555-6530. https://doi.org/10.1134/S1064230707060032.
- Молодцов Д.А. Начала рационального анализа – непрерывность функций // Нечеткие системы и мягкие вычисления. 2019. Т. 2. С. 126–141. ISSN 18194362. https://doi.org/10.26456/fssc57.
- Молодцов Д.А. Начала рационального анализа – производные и интегралы // Нечеткие системы и мягкие вычисления. 2020. Т. 15. № 1. С. 5–25. ISSN 1819-4362. https://doi.org/10.26456/fssc70.
- Acharjee S., Molodtsov D.A. Soft Rational Line Integral // Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki. 2021. V. 31. № 4. P. 578–596. ISSN 2076-5959, 1994-9197. https://doi.org/10.35634/vm210404.
- Молодцов Д.А. Мягкое дифференциальное уравнение // ЖВМиМФ. 2000. Т. 40. № 8. С. 1116–1128. ISSN 0965-5425.
- Maji P.K., Roy A.R., Biswas R. An Application of Soft Sets in a Decision Making Problem // Computers & Mathematics with Applications. 2002. V. 44. № 8. P. 1077–1083. ISSN 0898-1221. https://doi.org/10.1016/S0898-1221(02)00216-X.
- Aktas H., Cagman N. Soft Sets and Soft Groups // Information Sciences. 2007. V. 177. № 13. P. 2726–2735. ISSN 0020-0255, 1872-6291. https://doi.org/10.1016/j.ins.2006.12.008.
- Park C.H., Jun Y.B., Ozturk M.A. Soft WS-algebras // Communications of the Korean Mathematical Society. 2008. V. 23. № 3. P. 313–324. ISSN 1225-1763. https://doi.org/10.4134/CKMS.2008.23.3.313 ; Publisher: Korean Mathematical Society.
- Jun Y.B., Park C.H. Applications of Soft Sets in Ideal Theory of BCK/BCI-algebras // Information Sciences. 2008. V. 178. № 11. P. 2466– 2475. ISSN 0020-0255. https://doi.org/10.1016/j.ins.2008.01.017.
- Ma X., Zhan J., Xu Y. Lattice Implication Algebras Based on Soft Set Theory // Computational Intelligence. World Scientific, 2010. P. 535–540. ISBN 978-981-4324-69-4. https://doi.org/10.1142/9789814324700 0080.
- Liu Z., Alcantud J.C.R., Qin K., Xiong L. The Soft Sets and Fuzzy Sets-Based Neural Networks and Application // IEEE Access. 2020. V. 8. P. 41615–41625. https://doi.org/10.1109/ACCESS.2020.2976731.
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