phone +7 (3412) 91 60 92
mail imi@udsu.ru
ru-RU Russian
Home » Issues » Archive of Issues » 2023 - 1 issue » pp. 32-53

Archive of Issues

India Guwahati
Year
2023
Volume
33
Issue
1
Pages
32-53
<<
>>
Section Mathematics
Title Correct structures and similarity measures of soft sets along with historic comments of Prof. D.A. Molodtsov
Author(-s) Acharjee S.a, Oza A.a
Affiliations Gauhati Universitya
Abstract After the paper of Molodtsov [Molodtsov D. Soft set theory — First results, Computers and Mathematics with Applications, 1999, vol. 37, no. 4-5, pp. 19-31.] first appeared, soft set theory grew at a breakneck pace. Several authors have introduced various operations, relations, results, etc. as well as other aspects in soft set theory and hybrid structures incorrectly, despite their widespread use in mathematics and allied areas. In his paper [Molodtsov D.A. Equivalence and correct operations for soft sets, International Robotics and Automation Journal, 2018, vol. 4, no. 1, pp. 18-21.], Molodtsov, the father of soft set theory, pointed out several wrong results and notions. Molodtsov [Molodtsov D.A. Structure of soft sets, Nechetkie Sistemy i Myagkie Vychisleniya, 2017, vol. 12, no. 1, pp. 5-18.] also stated that the concept of soft set had not been fully understood and used everywhere. As a result, it is important to revisit the quirks of those conceptions and provide a formal account of the notion of soft set equivalency. Molodtsov already explored many correct operations on soft sets. We use some notions and results of Molodtsov [Molodtsov D.A. Structure of soft sets, Nechetkie Sistemy i Myagkie Vychisleniya, 2017, vol. 12, no. 1, pp. 5-18.] to create matrix representations as well as related operations of soft sets, and to quantify the similarity between two soft sets.
Keywords soft set, operations of soft sets, matrix representation, similarity measure
UDC 510.67, 004.8
MSC 03C99, 68T27, 68T09
DOI 10.35634/vm230103
Received 15 July 2022
Language English
Citation Acharjee S., Oza A. Correct structures and similarity measures of soft sets along with historic comments of Prof. D.A. Molodtsov, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 1, pp. 32-53.
References
  1. Molodtsov D. Soft set theory — First results, Computers and Mathematics with Applications, 1999, vol. 37, no. 4-5, pp. 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5
  2. Zadeh L.A. Fuzzy sets, Information and Control, 1965, vol. 8, no. 3, pp. 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  3. Aubin J.P., Frankowska H. Set-valued analysis, Boston: Birkhäuser, 1990.
  4. Acharjee S., Molodtsov D.A. Soft rational line integral, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, no. 4, pp. 578-596. https://doi.org/10.35634/vm210404
  5. Molodtsov D.A. Stability and regularization of optimality principles, USSR Computational Mathematics and Mathematical Physics, 1980, vol. 20, no. 5, pp. 25-38. https://doi.org/10.1016/0041-5553(80)90086-5
  6. Maji P.K., Roy A.R., Biswas R. An application of soft sets in a decision making problem, Computers and Mathematics with Applications, 2002, vol. 44, no. 8-9, pp. 1077-1083. https://doi.org/10.1016/S0898-1221(02)00216-X
  7. Maji P.K., Biswas R., Roy A.R. Soft set theory, Computers and Mathematics with Applications, 2003, vol. 45, no. 4-5, pp. 555-562. https://doi.org/10.1016/S0898-1221(03)00016-6
  8. Chen D., Tsang E.C.C., Yeung D.S., Wang X. The parameterization reduction of soft sets and its applications, Computers and Mathematics with Applications, 2005, vol. 49, no. 5-6, pp. 757-763. https://doi.org/10.1016/j.camwa.2004.10.036
  9. Majumdar P., Samanta S.K. Similarity measure of soft sets, New Mathematics and Natural Computation, 2008, vol. 4, no. 1, pp. 1-12. https://doi.org/10.1142/S1793005708000908
  10. Çağman N., Enginoğlu S. Soft matrix theory and its decision making, Computers and Mathematics with Applications, 2010, vol. 59, no. 10, pp. 3308-3314. https://doi.org/10.1016/j.camwa.2010.03.015
  11. Mondal S., Pal M. Soft matrices, African Journal of Mathematics and Computer Science Research, 2011, vol. 4, no. 13, pp. 379-388. https://academicjournals.org/journal/AJMCSR/article-abstract/A9EF6D33112
  12. Kharal A. Distance and similarity measures for soft sets, New Mathematics and Natural Computation, 2010, vol. 6, no. 3, pp. 321-334. https://doi.org/10.1142/S1793005710001724
  13. Kamaci H. Similarity measure for soft matrices and its applications, Journal of Intelligent and Fuzzy Systems: Applications in Engineering and Technology, 2019, vol. 36, no. 4, pp. 3061-3072. https://doi.org/10.3233/JIFS-18339
  14. Vijayabalaji S., Ramesh A. A new decision making theory in soft matrices, International Journal of Pure and Applied Mathematics, 2013, vol. 86, no. 6, pp. 927-939. https://www.ijpam.eu/contents/2013-86-6/6/index.html
  15. Molodtsov D.A. Equivalence and correct operations for soft sets, International Robotics and Automation Journal, 2018, vol. 4, no. 1, pp. 18-21. https://doi.org/10.15406/iratj.2018.04.00086
  16. Molodtsov D.A. Structure of soft sets, Nechetkie Sistemy i Myagkie Vychisleniya, 2017, vol. 12, no. 1, pp. 5-18 (in Russian). https://www.mathnet.ru/eng/fssc32
  17. https://www.researchgate.net/publication/328509865_Complex_Multi-Fuzzy_Soft_Set_Its_Entropy_and_Similarity_Measure/comments (Browsed on 02/07/2023)
  18. Al-Qudah Y., Hassan N. Complex multi-fuzzy soft set: Its entropy and similarity measure, IEEE Access, 2018, vol. 6, pp. 65002-65017. https://doi.org/10.1109/access.2018.2877921
  19. Acharjee S. New results for Kharal's similarity measures of soft sets, New Mathematics and Natural Computation, 2017, vol. 13, no. 1, pp. 55-60. https://doi.org/10.1142/S1793005717500053
  20. Acharjee S., Tripathy B.C. Some results on soft bitopology, Boletim da Sociedade Paranaense de Matemática, 2017, vol. 35, no. 1, pp. 269-279. https://doi.org/10.5269/bspm.v35i1.29145
  21. Yao J.T. Information granulation and granular relationships, 2005 IEEE International Conference on Granular Computing, IEEE, 2005, vol. 1, pp. 326-329. https://doi.org/10.1109/GRC.2005.1547296
  22. Bargiela A., Pedrycz W. Granular computing, Handbook on computational intelligence. Vol. 1. Fuzzy logic, systems, artificial neural networks, and learning systems, World Scientific, 2016, pp. 43-66. https://doi.org/10.1142/9789814675017_0002
  23. Yao Y. Artificial intelligence perspectives on granular computing, Granular computing and intelligent systems. Design with information granules of higher order and higher type, Berlin-Heidelberg: Springer, 2011, pp. 17-34. https://doi.org/10.1007/978-3-642-19820-5_2
  24. Belohlavek R., Klir G.J., Lewis III H.W., Way E.C. Concepts and fuzzy sets: Misunderstandings, misconceptions, and oversights, International Journal of Approximate Reasoning, 2009, vol. 51, no. 1, pp. 23-34. https://doi.org/10.1016/j.ijar.2009.06.012
  25. Shabir M., Naz M. On soft topological spaces, Computers and Mathematics with Applications, 2011, vol. 61, no. 7, pp. 1786-1799. https://doi.org/10.1016/j.camwa.2011.02.006
  26. Çağman N., Karataş S., Enginoglu S. Soft topology, Computers and Mathematics with Applications, 2011, vol. 62, no. 1, pp. 351-358. https://doi.org/10.1016/j.camwa.2011.05.016
  27. Hazra H., Majumdar P., Samanta S.K. Soft topology, Fuzzy Information and Engineering, 2012, vol. 4, no. 1, pp. 105-115. https://doi.org/10.1007/s12543-012-0104-2
  28. Varol B.P., Shostak A., Aygün H. A new approach to soft topology, Hacettepe Journal of Mathematics and Statistics, 2012, vol. 41, no. 5, pp. 731-741. https://dergipark.org.tr/en/pub/hujms/issue/7752/101326
Full text
/doc/issues-2023/23-01-03.pdf
<< Previous article
Next article >>