Research Article
BibTex RIS Cite

Bijective soft rings with applications

Year 2024, , 47 - 60, 30.04.2024
https://doi.org/10.54187/jnrs.1464556

Abstract

In recent years, soft sets have been widely used in many important decision-making real-life problems. In this paper, observing the usage of soft sets in such kind of vital problems, we have introduced the bijective-unitary bijective soft rings. Firstly, we have defined and exemplified a bijective soft ring and a unitary bijective soft ring. Moreover, we have presented some applications of bijective soft rings. We have shown the usage of bijective soft rings in coding theory. In this context, we have observed that by obtaining a bijective soft ring over a finite ring, we have a coding matrix to encode a given set of messages. Besides these applicable results, we have also obtained some relations between bijective soft and classical rings.

References

  • D. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications 37 (4-5) 1999 19-31.
  • P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Computers and Mathematics with Applications 44 (8-9) (2002) 1077-1083.
  • P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Computers and Mathematics with Applications 45 (4-5) (2003) 555-562.
  • D. Chen, E. C. C. Tsang, D. S. Yeung, X. Wang, The parameterization reduction of soft sets and its applications Computers and Mathematics with Applications 49 (5-6) (2005) 757-763.
  • H. Aktaş, N. Çağman, Soft sets and soft groups, Information Sciences 177 (11) (2007) 2726-2735.
  • Q. M. Sun, Z. L. Zhang, J. Liu, Soft sets and soft modules, in: Wang, G., Li, T., Grzymala-Busse, J. W., Miao, D., Skowron, A., Yao, Y. (Eds.) Rough Sets and Knowledge Technology, Springer, Berlin, Heidelberg, 2008, pp. 403-409.
  • F. Feng, Y. B. Jun, X. Zhao, Soft semirings, Computers and Mathematics with Applications 56 (10) 2008 2621-2628.
  • Y. B. Jun, C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Information Sciences 178 (11) (2008) 2466-2475.
  • M. I. Ali, F. Feng, X. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Computer and Mathematics with Applications 57 (9) (2009) 1547-1553.
  • M. I. Ali, M. Shabir, M. Naz, Algebraic structures of soft sets associated with new operations, Computer and Mathematics with Applications 61 (9) (2011) 2647-2654.
  • A. Aygünoğlu, H. Aygün, Introduction to fuzzy soft groups, Computer and Mathematics with Applications 58 (6) (2009) 1279-1286.
  • O. Kazancı, S. Yılmaz, S. Yamak, Soft sets and soft BCH-algebras, Hacettepe Journal of Mathematics and Statistics 39 (2) (2010) 205-217.
  • N. Çağman, S. Enginoğlu, Soft set theory and uni-int decision making, European Journal of Operational Research 207 (2) 2010 848-855.
  • K. V. Babitha, J. J. Sunil, Soft set relations and functions Computers and Mathematics with Applications 60 (7) 2010 1840-1849.
  • Z. Xiao, K. Gong, S. Xia, Y. Zou, Exclusive disjunctive soft sets, Computers and Mathematics with Applications 59 (6) (2010) 2128-2137.
  • K. Gong, Z. Xiao, X. Zhang, The bijective soft set with its operations, Computers and Mathematics with Applications 60 (8) (2010) 2270-2278.
  • U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Computers and Mathematics with Applications 59 (11) (2010) 3458-3463.
  • F. Feng, X. Liu, V. L. Fotea, Y. B. Jun, Soft sets and soft rough sets, Information Sciences 181 (6) 2011 1125-1137.
  • A. O. Atagün, A. Sezgin, Soft substructures of rings, fields and modules, Computer and Mathematics with Applications, 61 (3) (2011) 592-601.
  • I. Deli, N. Çağman, Intuitionistic fuzzy parameterized soft set theory and its decision making, Applied Soft Computing 28 (2015) 109-113.
  • H. Aktaş, Some algebraic applications of soft sets, Applied Soft Computing 28 (2015) 327-331.
  • F. Koyuncu, B. Tanay, Some soft algebraic structures, Journal of New Results in Science 10 (2016) 38-51.
  • P. Chaipunya, P. Kumam, On some classical soft intersection properties, Journal of Nonlinear Science and Applications 9 (2016) 5136-5142.
  • M. Ali, H. Khan, L. H. Son, F. Smarandache, W. B. V. Kandasamy, New soft set based class of linear algebraic codes, Symmetry 10 (2018) 510.
  • S. Goldar, S. Ray, A classical view of soft ring and soft ideal, Journal of Applied Science and Computations 6 (3) (2019) 1457-1467.
  • S. Öztunç, S. Aslan, H. Dutta, Categorical structures of soft groups, Soft Computing 25 (2021) 3059-3064.
  • R. Anjum, A. R. K. Lodhi, M. Munir, N. Kausar, Soft intersection and soft union k-ideals of hemirings and their applications, Korean Journal of Mathematics 30 (2) (2022) 263-281.
  • E. Aygün, H. Kamacı, Two different types of soft near-fields, Punjab University Journal of Mathematics 54 (7) (2022) 429-440.
  • R. Nagarajan, A. Prabakaran, Certain representations on soft M-N modulo theory, International Journal of Engineering, Science and Mathematics 12 (1) (2023) 66-76.
Year 2024, , 47 - 60, 30.04.2024
https://doi.org/10.54187/jnrs.1464556

Abstract

References

  • D. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications 37 (4-5) 1999 19-31.
  • P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Computers and Mathematics with Applications 44 (8-9) (2002) 1077-1083.
  • P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Computers and Mathematics with Applications 45 (4-5) (2003) 555-562.
  • D. Chen, E. C. C. Tsang, D. S. Yeung, X. Wang, The parameterization reduction of soft sets and its applications Computers and Mathematics with Applications 49 (5-6) (2005) 757-763.
  • H. Aktaş, N. Çağman, Soft sets and soft groups, Information Sciences 177 (11) (2007) 2726-2735.
  • Q. M. Sun, Z. L. Zhang, J. Liu, Soft sets and soft modules, in: Wang, G., Li, T., Grzymala-Busse, J. W., Miao, D., Skowron, A., Yao, Y. (Eds.) Rough Sets and Knowledge Technology, Springer, Berlin, Heidelberg, 2008, pp. 403-409.
  • F. Feng, Y. B. Jun, X. Zhao, Soft semirings, Computers and Mathematics with Applications 56 (10) 2008 2621-2628.
  • Y. B. Jun, C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Information Sciences 178 (11) (2008) 2466-2475.
  • M. I. Ali, F. Feng, X. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Computer and Mathematics with Applications 57 (9) (2009) 1547-1553.
  • M. I. Ali, M. Shabir, M. Naz, Algebraic structures of soft sets associated with new operations, Computer and Mathematics with Applications 61 (9) (2011) 2647-2654.
  • A. Aygünoğlu, H. Aygün, Introduction to fuzzy soft groups, Computer and Mathematics with Applications 58 (6) (2009) 1279-1286.
  • O. Kazancı, S. Yılmaz, S. Yamak, Soft sets and soft BCH-algebras, Hacettepe Journal of Mathematics and Statistics 39 (2) (2010) 205-217.
  • N. Çağman, S. Enginoğlu, Soft set theory and uni-int decision making, European Journal of Operational Research 207 (2) 2010 848-855.
  • K. V. Babitha, J. J. Sunil, Soft set relations and functions Computers and Mathematics with Applications 60 (7) 2010 1840-1849.
  • Z. Xiao, K. Gong, S. Xia, Y. Zou, Exclusive disjunctive soft sets, Computers and Mathematics with Applications 59 (6) (2010) 2128-2137.
  • K. Gong, Z. Xiao, X. Zhang, The bijective soft set with its operations, Computers and Mathematics with Applications 60 (8) (2010) 2270-2278.
  • U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Computers and Mathematics with Applications 59 (11) (2010) 3458-3463.
  • F. Feng, X. Liu, V. L. Fotea, Y. B. Jun, Soft sets and soft rough sets, Information Sciences 181 (6) 2011 1125-1137.
  • A. O. Atagün, A. Sezgin, Soft substructures of rings, fields and modules, Computer and Mathematics with Applications, 61 (3) (2011) 592-601.
  • I. Deli, N. Çağman, Intuitionistic fuzzy parameterized soft set theory and its decision making, Applied Soft Computing 28 (2015) 109-113.
  • H. Aktaş, Some algebraic applications of soft sets, Applied Soft Computing 28 (2015) 327-331.
  • F. Koyuncu, B. Tanay, Some soft algebraic structures, Journal of New Results in Science 10 (2016) 38-51.
  • P. Chaipunya, P. Kumam, On some classical soft intersection properties, Journal of Nonlinear Science and Applications 9 (2016) 5136-5142.
  • M. Ali, H. Khan, L. H. Son, F. Smarandache, W. B. V. Kandasamy, New soft set based class of linear algebraic codes, Symmetry 10 (2018) 510.
  • S. Goldar, S. Ray, A classical view of soft ring and soft ideal, Journal of Applied Science and Computations 6 (3) (2019) 1457-1467.
  • S. Öztunç, S. Aslan, H. Dutta, Categorical structures of soft groups, Soft Computing 25 (2021) 3059-3064.
  • R. Anjum, A. R. K. Lodhi, M. Munir, N. Kausar, Soft intersection and soft union k-ideals of hemirings and their applications, Korean Journal of Mathematics 30 (2) (2022) 263-281.
  • E. Aygün, H. Kamacı, Two different types of soft near-fields, Punjab University Journal of Mathematics 54 (7) (2022) 429-440.
  • R. Nagarajan, A. Prabakaran, Certain representations on soft M-N modulo theory, International Journal of Engineering, Science and Mathematics 12 (1) (2023) 66-76.
There are 29 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Articles
Authors

Fatih Koyuncu 0000-0001-6351-4787

Publication Date April 30, 2024
Submission Date April 3, 2024
Acceptance Date April 29, 2024
Published in Issue Year 2024

Cite

APA Koyuncu, F. (2024). Bijective soft rings with applications. Journal of New Results in Science, 13(1), 47-60. https://doi.org/10.54187/jnrs.1464556
AMA Koyuncu F. Bijective soft rings with applications. JNRS. April 2024;13(1):47-60. doi:10.54187/jnrs.1464556
Chicago Koyuncu, Fatih. “Bijective Soft Rings With Applications”. Journal of New Results in Science 13, no. 1 (April 2024): 47-60. https://doi.org/10.54187/jnrs.1464556.
EndNote Koyuncu F (April 1, 2024) Bijective soft rings with applications. Journal of New Results in Science 13 1 47–60.
IEEE F. Koyuncu, “Bijective soft rings with applications”, JNRS, vol. 13, no. 1, pp. 47–60, 2024, doi: 10.54187/jnrs.1464556.
ISNAD Koyuncu, Fatih. “Bijective Soft Rings With Applications”. Journal of New Results in Science 13/1 (April 2024), 47-60. https://doi.org/10.54187/jnrs.1464556.
JAMA Koyuncu F. Bijective soft rings with applications. JNRS. 2024;13:47–60.
MLA Koyuncu, Fatih. “Bijective Soft Rings With Applications”. Journal of New Results in Science, vol. 13, no. 1, 2024, pp. 47-60, doi:10.54187/jnrs.1464556.
Vancouver Koyuncu F. Bijective soft rings with applications. JNRS. 2024;13(1):47-60.


TR Dizin 31688

EBSCO30456


Electronic Journals Library EZB   30356

 DOAJ   30355                                             

WorldCat  30357                                             303573035530355

Academindex   30358

SOBİAD   30359

Scilit   30360


29388 As of 2021, JNRS is licensed under a Creative Commons Attribution-NonCommercial 4.0 International Licence (CC BY-NC).