Araştırma Makalesi
Yıl 2024,
Cilt: 13 Sayı: 1, 47 - 60, 30.04.2024
Öz
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.
Anahtar Kelimeler
Soft sets Soft rings Bijective soft sets Bijective soft rings Unitary bijective soft rings
Kaynakça
- 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.
Yıl 2024,
Cilt: 13 Sayı: 1, 47 - 60, 30.04.2024
Öz
Kaynakça
- 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.
Toplam 29 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebir ve Sayı Teorisi |
| Bölüm | Articles |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Nisan 2024 |
| Gönderilme Tarihi | 3 Nisan 2024 |
| Kabul Tarihi | 29 Nisan 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 13 Sayı: 1 |
Kaynak Göster
EBSCO |
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