Araştırma Makalesi
BibTex RIS Kaynak Göster

Set-generated soft subrings of rings

Yıl 2022, Cilt: 71 Sayı: 4, 993 - 1006, 30.12.2022

Akın Osman Atagün , Hüseyin Kamacı

https://doi.org/10.31801/cfsuasmas.1013172

Öz

This paper focuses on the set-oriented operations and set-oriented algebraic structures of soft sets. Relatedly, in this paper, firstly some essential properties of $\alpha$-intersection of soft set are investigated, where $\alpha$ is a non-empty subset of the universal set. Later, by using $\alpha$-intersection of soft set, the notion of set-generated soft subring of a ring is introduced. The generators of soft intersections and products of soft subrings are given. Some related properties about generators of soft subrings are investigated and illustrated by several examples.

Anahtar Kelimeler

Soft sets soft subrings of rings generated soft subrings of rings

Kaynakça

  • Zadeh, L. A., Fuzzy sets, Inf. Control, 8 (1965), 338–353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
  • Zadeh, L. A., Toward a generalized theory of uncertainty (GTU)-an outline, Inf. Sci., 172 (2005), 1–40. https://doi.org/10.1016/j.ins.2005.01.017
  • Gorzalzany, M. B., A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets Syst., 21 (1987), 1–17. https://doi.org/10.1016/0165-0114(87)90148-5
  • Gau, W. L., Buehrer, D. J., Vague sets, IEEE Trans. Syst. Man Cybern., 23 (1993), 610–614. doi: 10.1109/21.229476
  • Pawlak, Z., Rough sets, Int. J. Comput. Inf. Sci., 11 (1982), 341–356. http://dx.doi.org/10.1007/BF01001956
  • Pawlak, Z., Skowron, A., Rudiments of rough sets, Inf. Sci., 177 (2007), 3–27. doi:10.1016/j.ins.2006.06.003
  • Molodtsov, D., Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5
  • Maji, P. K., Biswas, R., Roy, A. R., Soft set theory, Comput. Math. Appl., 45 (2003), 555–562. https://doi.org/10.1016/S0898-1221(03)00016-6
  • Maji, P. K., Roy, A. R., Biswas, R., An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002), 1077–1083. https://doi.org/10.1016/S0898-1221(02)00216-X
  • Ali, M. I., Feng, F., Liu, X., Min, W. K., Shabir, M., On some new operations in soft set theory, Comput. Math. Appl., 57 (2009), 1547–1553. https://doi.org/10.1016/j.camwa.2008.11.009
  • Çağman, N., Enginoğlu, S., Soft set theory and uni-int decision making, Eur. J. Oper. Res., 207 (2010), 848–855. https://doi.org/10.1016/j.ejor.2010.05.004
  • Kamacı, H., Similarity measure for soft matrices and its applications, J. Intell. Fuzzy Syst., 36 (2019), 3061–3072. doi: 10.3233/JIFS-18339
  • Kamacı, H., Atagün, A. O., Aygün, E., Difference operations of soft matrices with applications in decision making, Punjab Univ. J. Math., 51 (2019), 1–21.
  • Sezgin, A., Atagün, A. O., On operations of soft sets, Comput. Math. Appl., 61 (2011), 1457–1467.https://doi.org/10.1016/j.camwa.2011.01.018
  • Aygün, E., Kamacı, H., Some generalized operations in soft set theory and their role in similarity and decision making, J. Intell. Fuzzy Syst., 36 (2019), 6537–6547. doi: 10.3233/JIFS-182924
  • Aygün, E., Kamacı, H., Some new algebraic structures of soft sets, Soft Comput., 25(13) (2021), 8609–8626. https://doi.org/10.1007/s00500-021-05744-y
  • Çağman, N., Enginoğlu, S., Soft matrix theory and its decision making, Comput. Math. Appl., 59 (2010), 3308–3314. https://doi.org/10.1016/j.camwa.2010.03.015
  • Atagün, A. O., Kamacı, H., Oktay, O., Reduced soft matrices and generalized products with applications in decision making, Neural Comput. Appl., 29 (2018), 445–456. https://doi.org/10.1007/s00521-016-2542-y
  • Kamacı, H., Atagün, A. O., Sönmezoğlu, A., Row-products of soft matrices with applications in multiple-disjoint decision making, Appl. Soft Comput., 62 (2018), 892–914. https://doi.org/10.1016/j.asoc.2017.09.024
  • Kamacı, H., Atagün, A. O., Toktaş, E., Bijective soft matrix theory and multi-bijective linguistic soft decision system, Filomat, 32 (2018), 3799–3814. https://doi.org/10.2298/FIL1811799K
  • Petchimuthu, S., Garg, H., Kamacı, H., Atagün, A. O., The mean operators and generalized products of fuzzy soft matrices and their applications in MCGDM, Comput. Appl. Math., 39 (2020), Article Number 68. https://doi.org/10.1007/s40314-020-1083-2
  • Kamacı, H., Saltık, K., Akız, H. F., Atagün, A. O., Cardinality inverse soft matrix theory and its applications in multicriteria group decision making, J. Intell. Fuzzy Syst., 34 (2018), 2031–2049. doi: 10.3233/JIFS-17876
  • Petchimuthu, S., Kamacı, H., The row-products of inverse soft matrices in multicriteria decision making, J. Intell. Fuzzy Syst., 36 (2019), 6425–6441. doi: 10.3233/JIFS-182709
  • Aktaş, H., Çağman, N., Soft sets and soft groups, Inf. Sci., 177 (2007), 2726–2735. https://doi.org/10.1016/j.ins.2006.12.008
  • Ulucay, V., Oztekin, O., Sahin, M., Olgun, N., Kargin, A., Soft representation of soft groups, New Trend Math. Sci., 4(2) (2016), 23. http://dx.doi.org/10.20852/ntmsci.2016217001
  • Feng, F., Jun, Y. B., Zhao, X., Soft semirings, Comput. Math. Appl., 56 (2008), 2621–2628. https://doi.org/10.1016/j.camwa.2008.05.011
  • Acar, U., Koyuncu, F., Tanay, B., Soft sets and soft rings, Comput. Math. Appl., 59 (2010), 3458-3463. https://doi.org/10.1016/j.camwa.2010.03.034
  • Uluçay, V., Şahin, M., Olgun, N., Soft normed rings, SpringerPlus, 5(1) (2016), 1–6. doi: 10.1186/s40064-016-3636-9
  • Atagün, A. O., Sezer, A. S., Soft substructures of rings fields and modules, Comput. Math. Appl., 61 (2011), 592–601. https://doi.org/10.1016/j.camwa.2010.12.005
  • Sezgin, A., Atagün, A. O., Aygün, E., A note on soft near-rings and idealistic soft near-rings, Filomat, 25 (2011), 53–68. doi: 10.2298/FIL1101053S
  • Ostadhadi-Dehkordi, S., Shum, K. P., Regular and strongly regular relations on soft hyperrings, Soft Comput., 23 (2019), 3253–3260. https://doi.org/10.1007/s00500-018-03711-8
  • Tahat, M. K., Sidky, F., Abo-Elhamayel, M., Soft topological soft groups and soft rings, Soft Comput., 22 (2018), 7143–7156. https://doi.org/10.1007/s00500-018-3026-z
  • Karaaslan, F., Some properties of AG*-groupoids and AG-bands under SI-product operation, J. Intell. Fuzzy Syst., 36 (2019), 231–239. doi: 10.3233/JIFS-181208
  • Yousafzaia, F., Khalaf, M. M., Alia, A., Arsham B., Saeidc, D., Non-associative ordered semigroups based on soft sets, Commun. Algebra, 47 (2019), 312–327. https://doi.org/10.1080/00927872.2018.1476524
  • Zhan, J., Dudek, W. A., Neggers, J., A new soft union set: characterizations of hemirings, Int. J. Mach. Learn. Cybern., 8 (2017), 525–535. https://doi.org/10.1007/s13042-015-0343-8
  • Atagün, A. O., Sezgin, A., Soft subnear-rings, soft ideals and soft N-subgroups of near-rings, Math. Sci. Lett., 7 (2018), 37–42. http://dx.doi.org/10.18576/msl/070106
  • Riaz, M., Naeem, K., Aslam, M., Afzal, D., Almahdi, F. A. A., Jamal, S. S., Multi-criteria group decision making with Pythagorean fuzzy soft topology, J. Intell. Fuzzy Syst., 39 (2020), 6703–6720. doi: 10.3233/JIFS-190854
  • Riaz, M., Naim, Ç., Zareef, I., Aslam, M., N-soft topology and its applications to multi-criteria group decision making, J. Intell. Fuzzy Syst., 36 (2019), 6521–6536. doi: 10.3233/JIFS-182919
  • Riaz, M., Tehreim, S. T., On bipolar fuzzy soft topology with decision-making, Soft Comput., 24 (2020), 18259–18272. https://doi.org/10.1007/s00500-020-05342-4
  • Sezer, A. S., Çağman, N., Atagün, A. O., Ali, M. I., Türkmen, E., Soft intersection semigroups, ideals and bi-ideals; a new application on semigroup theory I, Filomat, 29 (2015), 917–946. doi: 10.2298/FIL1505917S
  • Sezgin, A., Çağman, N., Çıtak, F., α-inclusions applied to group theory via soft set and logic, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68 (2019), 334–352. doi: 10.31801/cfsuasmas.420457
  • Feng, F., Li, C. X., Davvaz, B., Ali, M. I., Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Comput., 14 (2010), 899–911. https://doi.org/10.1007/s00500-009-0465-6
  • Feng, F., Liu, X. Y., Leoreanu-Fotea, V., Jun, Y. B., Soft sets and soft rough sets, Inf. Sci., 181 (2011), 1125–1137. https://doi.org/10.1016/j.ins.2010.11.004
  • Atagün, A. O., Kamacı, H., Decompositions of soft sets and soft matrices with applications in group decision making, Scientia Iranica, in press (2021). doi:10.24200/SCI.2021.58119.5575.

Yıl 2022, Cilt: 71 Sayı: 4, 993 - 1006, 30.12.2022

Akın Osman Atagün , Hüseyin Kamacı

https://doi.org/10.31801/cfsuasmas.1013172

Öz

Kaynakça

  • Zadeh, L. A., Fuzzy sets, Inf. Control, 8 (1965), 338–353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
  • Zadeh, L. A., Toward a generalized theory of uncertainty (GTU)-an outline, Inf. Sci., 172 (2005), 1–40. https://doi.org/10.1016/j.ins.2005.01.017
  • Gorzalzany, M. B., A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets Syst., 21 (1987), 1–17. https://doi.org/10.1016/0165-0114(87)90148-5
  • Gau, W. L., Buehrer, D. J., Vague sets, IEEE Trans. Syst. Man Cybern., 23 (1993), 610–614. doi: 10.1109/21.229476
  • Pawlak, Z., Rough sets, Int. J. Comput. Inf. Sci., 11 (1982), 341–356. http://dx.doi.org/10.1007/BF01001956
  • Pawlak, Z., Skowron, A., Rudiments of rough sets, Inf. Sci., 177 (2007), 3–27. doi:10.1016/j.ins.2006.06.003
  • Molodtsov, D., Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5
  • Maji, P. K., Biswas, R., Roy, A. R., Soft set theory, Comput. Math. Appl., 45 (2003), 555–562. https://doi.org/10.1016/S0898-1221(03)00016-6
  • Maji, P. K., Roy, A. R., Biswas, R., An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002), 1077–1083. https://doi.org/10.1016/S0898-1221(02)00216-X
  • Ali, M. I., Feng, F., Liu, X., Min, W. K., Shabir, M., On some new operations in soft set theory, Comput. Math. Appl., 57 (2009), 1547–1553. https://doi.org/10.1016/j.camwa.2008.11.009
  • Çağman, N., Enginoğlu, S., Soft set theory and uni-int decision making, Eur. J. Oper. Res., 207 (2010), 848–855. https://doi.org/10.1016/j.ejor.2010.05.004
  • Kamacı, H., Similarity measure for soft matrices and its applications, J. Intell. Fuzzy Syst., 36 (2019), 3061–3072. doi: 10.3233/JIFS-18339
  • Kamacı, H., Atagün, A. O., Aygün, E., Difference operations of soft matrices with applications in decision making, Punjab Univ. J. Math., 51 (2019), 1–21.
  • Sezgin, A., Atagün, A. O., On operations of soft sets, Comput. Math. Appl., 61 (2011), 1457–1467.https://doi.org/10.1016/j.camwa.2011.01.018
  • Aygün, E., Kamacı, H., Some generalized operations in soft set theory and their role in similarity and decision making, J. Intell. Fuzzy Syst., 36 (2019), 6537–6547. doi: 10.3233/JIFS-182924
  • Aygün, E., Kamacı, H., Some new algebraic structures of soft sets, Soft Comput., 25(13) (2021), 8609–8626. https://doi.org/10.1007/s00500-021-05744-y
  • Çağman, N., Enginoğlu, S., Soft matrix theory and its decision making, Comput. Math. Appl., 59 (2010), 3308–3314. https://doi.org/10.1016/j.camwa.2010.03.015
  • Atagün, A. O., Kamacı, H., Oktay, O., Reduced soft matrices and generalized products with applications in decision making, Neural Comput. Appl., 29 (2018), 445–456. https://doi.org/10.1007/s00521-016-2542-y
  • Kamacı, H., Atagün, A. O., Sönmezoğlu, A., Row-products of soft matrices with applications in multiple-disjoint decision making, Appl. Soft Comput., 62 (2018), 892–914. https://doi.org/10.1016/j.asoc.2017.09.024
  • Kamacı, H., Atagün, A. O., Toktaş, E., Bijective soft matrix theory and multi-bijective linguistic soft decision system, Filomat, 32 (2018), 3799–3814. https://doi.org/10.2298/FIL1811799K
  • Petchimuthu, S., Garg, H., Kamacı, H., Atagün, A. O., The mean operators and generalized products of fuzzy soft matrices and their applications in MCGDM, Comput. Appl. Math., 39 (2020), Article Number 68. https://doi.org/10.1007/s40314-020-1083-2
  • Kamacı, H., Saltık, K., Akız, H. F., Atagün, A. O., Cardinality inverse soft matrix theory and its applications in multicriteria group decision making, J. Intell. Fuzzy Syst., 34 (2018), 2031–2049. doi: 10.3233/JIFS-17876
  • Petchimuthu, S., Kamacı, H., The row-products of inverse soft matrices in multicriteria decision making, J. Intell. Fuzzy Syst., 36 (2019), 6425–6441. doi: 10.3233/JIFS-182709
  • Aktaş, H., Çağman, N., Soft sets and soft groups, Inf. Sci., 177 (2007), 2726–2735. https://doi.org/10.1016/j.ins.2006.12.008
  • Ulucay, V., Oztekin, O., Sahin, M., Olgun, N., Kargin, A., Soft representation of soft groups, New Trend Math. Sci., 4(2) (2016), 23. http://dx.doi.org/10.20852/ntmsci.2016217001
  • Feng, F., Jun, Y. B., Zhao, X., Soft semirings, Comput. Math. Appl., 56 (2008), 2621–2628. https://doi.org/10.1016/j.camwa.2008.05.011
  • Acar, U., Koyuncu, F., Tanay, B., Soft sets and soft rings, Comput. Math. Appl., 59 (2010), 3458-3463. https://doi.org/10.1016/j.camwa.2010.03.034
  • Uluçay, V., Şahin, M., Olgun, N., Soft normed rings, SpringerPlus, 5(1) (2016), 1–6. doi: 10.1186/s40064-016-3636-9
  • Atagün, A. O., Sezer, A. S., Soft substructures of rings fields and modules, Comput. Math. Appl., 61 (2011), 592–601. https://doi.org/10.1016/j.camwa.2010.12.005
  • Sezgin, A., Atagün, A. O., Aygün, E., A note on soft near-rings and idealistic soft near-rings, Filomat, 25 (2011), 53–68. doi: 10.2298/FIL1101053S
  • Ostadhadi-Dehkordi, S., Shum, K. P., Regular and strongly regular relations on soft hyperrings, Soft Comput., 23 (2019), 3253–3260. https://doi.org/10.1007/s00500-018-03711-8
  • Tahat, M. K., Sidky, F., Abo-Elhamayel, M., Soft topological soft groups and soft rings, Soft Comput., 22 (2018), 7143–7156. https://doi.org/10.1007/s00500-018-3026-z
  • Karaaslan, F., Some properties of AG*-groupoids and AG-bands under SI-product operation, J. Intell. Fuzzy Syst., 36 (2019), 231–239. doi: 10.3233/JIFS-181208
  • Yousafzaia, F., Khalaf, M. M., Alia, A., Arsham B., Saeidc, D., Non-associative ordered semigroups based on soft sets, Commun. Algebra, 47 (2019), 312–327. https://doi.org/10.1080/00927872.2018.1476524
  • Zhan, J., Dudek, W. A., Neggers, J., A new soft union set: characterizations of hemirings, Int. J. Mach. Learn. Cybern., 8 (2017), 525–535. https://doi.org/10.1007/s13042-015-0343-8
  • Atagün, A. O., Sezgin, A., Soft subnear-rings, soft ideals and soft N-subgroups of near-rings, Math. Sci. Lett., 7 (2018), 37–42. http://dx.doi.org/10.18576/msl/070106
  • Riaz, M., Naeem, K., Aslam, M., Afzal, D., Almahdi, F. A. A., Jamal, S. S., Multi-criteria group decision making with Pythagorean fuzzy soft topology, J. Intell. Fuzzy Syst., 39 (2020), 6703–6720. doi: 10.3233/JIFS-190854
  • Riaz, M., Naim, Ç., Zareef, I., Aslam, M., N-soft topology and its applications to multi-criteria group decision making, J. Intell. Fuzzy Syst., 36 (2019), 6521–6536. doi: 10.3233/JIFS-182919
  • Riaz, M., Tehreim, S. T., On bipolar fuzzy soft topology with decision-making, Soft Comput., 24 (2020), 18259–18272. https://doi.org/10.1007/s00500-020-05342-4
  • Sezer, A. S., Çağman, N., Atagün, A. O., Ali, M. I., Türkmen, E., Soft intersection semigroups, ideals and bi-ideals; a new application on semigroup theory I, Filomat, 29 (2015), 917–946. doi: 10.2298/FIL1505917S
  • Sezgin, A., Çağman, N., Çıtak, F., α-inclusions applied to group theory via soft set and logic, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68 (2019), 334–352. doi: 10.31801/cfsuasmas.420457
  • Feng, F., Li, C. X., Davvaz, B., Ali, M. I., Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Comput., 14 (2010), 899–911. https://doi.org/10.1007/s00500-009-0465-6
  • Feng, F., Liu, X. Y., Leoreanu-Fotea, V., Jun, Y. B., Soft sets and soft rough sets, Inf. Sci., 181 (2011), 1125–1137. https://doi.org/10.1016/j.ins.2010.11.004
  • Atagün, A. O., Kamacı, H., Decompositions of soft sets and soft matrices with applications in group decision making, Scientia Iranica, in press (2021). doi:10.24200/SCI.2021.58119.5575.
Toplam 44 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Akın Osman Atagün 0000-0002-2131-9980

Hüseyin Kamacı 0000-0002-0429-6713

Yayımlanma Tarihi 30 Aralık 2022
Gönderilme Tarihi 21 Ekim 2021
Kabul Tarihi 18 Mayıs 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 71 Sayı: 4

Kaynak Göster

APA Atagün, A. O., & Kamacı, H. (2022). Set-generated soft subrings of rings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(4), 993-1006. https://doi.org/10.31801/cfsuasmas.1013172
AMA Atagün AO, Kamacı H. Set-generated soft subrings of rings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2022;71(4):993-1006. doi:10.31801/cfsuasmas.1013172
Chicago Atagün, Akın Osman, ve Hüseyin Kamacı. “Set-Generated Soft Subrings of Rings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, sy. 4 (Aralık 2022): 993-1006. https://doi.org/10.31801/cfsuasmas.1013172.
EndNote Atagün AO, Kamacı H (01 Aralık 2022) Set-generated soft subrings of rings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 4 993–1006.
IEEE A. O. Atagün ve H. Kamacı, “Set-generated soft subrings of rings”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 71, sy. 4, ss. 993–1006, 2022, doi: 10.31801/cfsuasmas.1013172.
ISNAD Atagün, Akın Osman - Kamacı, Hüseyin. “Set-Generated Soft Subrings of Rings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/4 (Aralık 2022), 993-1006. https://doi.org/10.31801/cfsuasmas.1013172.
JAMA Atagün AO, Kamacı H. Set-generated soft subrings of rings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:993–1006.
MLA Atagün, Akın Osman ve Hüseyin Kamacı. “Set-Generated Soft Subrings of Rings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 71, sy. 4, 2022, ss. 993-1006, doi:10.31801/cfsuasmas.1013172.
Vancouver Atagün AO, Kamacı H. Set-generated soft subrings of rings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(4):993-1006.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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