α-inclusions applied to group theory via soft set and logic

Aslıhan Sezgin; Naim Çağman; Filiz Çıtak

doi:10.31801/cfsuasmas.420457

Araştırma Makalesi

α-inclusions applied to group theory via soft set and logic

Yıl 2019, Cilt: 68 Sayı: 1, 334 - 352, 01.02.2019

Aslıhan Sezgin Naim Çağman Filiz Çıtak

https://doi.org/10.31801/cfsuasmas.420457

Cited By: 14

Öz

Soft set theory, initiated by Molodtsov, is a tool for modeling various types of uncertainty. In this paper, upper and lower α-inclusions of a soft set are defined. By using these new notions, some analyzes with respect to group theory are made and it is shown that some of the subgroups of a group can be obtained easily with the help of these notions. It is also illustrated that a soft int-group and a soft uni-group can be obtained by its upper α-subgroups and lower α-subgroups, respectively. Furthermore, soft int-group by its family of upper α-subgroups is characterized under a certain equivalence relation. Finally, a new method used to construct a soft int-group with the help of its upper α-subgroups are introduced and an application of this method is given.

Anahtar Kelimeler

Soft sets, soft int-groups, soft uni-groups, α-inclusions, α-subgroup

Kaynakça

Molodtsov, D., Soft set theory-first results, Comput. Math. Appl. 37, (1999), 19-31.
Maji, P.K., Biswas R. and Roy, A.R., Soft set theory, Comput. Math. Appl. 45, (2003), 555-562.
Ali, M.I., Feng, F., Liu, X., Min, W.K, and Shabir, M., On some new operations in soft set theory, Comput. Math. Appl. 57, (2009), 1547-1553.
Sezgin A., and Atagün, A.O, On operations of soft sets, Comput. Math. Appl. 61(5), (2011), 1457-1467.
Cağman, N., and Enginoğlu S., Soft matrix theory and its decision making, Comput. Math. Appl. 59, (2010) 3308-3314.
Cağman, N. and Enginoğlu, S. Soft set theory and uni-int decision making, Eur. J. Oper. Res. 207, (2010) 848-855.
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.
Molodtsov, D.A., Yu., V, Leonov and Kovkov, D. V., Soft sets technique and its application, Nechetkie Sistemi i Myakie Vychisleniya 1-1 (2006), 8-39.
Zou, Y. and Xiao, Z., Data analysis approaches of soft sets under incomplete information, Knowledge Based Systems 21, (2008), 941-945.
Zhan, J. Liu, Q., Herawan, T.,A novel soft rough set: soft rough hemirings and its multicriteria group decision making, Applied Soft Computing 54, (2017), 393--402.
Ma, X., Liu, Q., Zhan, J., A survey of decision making methods based on certain hybrid soft set models, Artificial Intelligence Review 47, (2017), 507--530.
Zhan, J., Zhu, K., A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Computing 21, (2017), 1923--1936.
Zhan, J., Ali, M.I, Mehmood, N., On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods, Applied Soft Computing 56, (2017), 446--457.
Aktas, H. and Cağman, N., Soft sets and soft groups, Inform. Sci. 177, (2007), 2726-2735.
Feng, F., Jun, Y.B. and X. Zhao, Soft semirings, Comput. Math. Appl. 56, (2008), 2621-2628.
Jun, Y.B., Soft BCK/BCI-algebras, Comput. Math. Appl. 56, (2008), 1408-1413.
Jun, Y.B and Park, C.H., Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci. 178, (2008), 2466-2475.
Jun, Y.B., Lee, K.J. and Zhan, J. Soft p-ideals of soft BCI-algebras, Comput. Math. Appl. 58, (2009), 2060-2068.
Kazancı, O., Yılmaz, S. and Yamak, S., Soft sets and soft BCH-algebras, Hacet. J. Math. Stat. 39, (2), (2010), 205-217.
Acar, U., Koyuncu, F. and Tanay, B., Soft sets and soft rings, Comput. Math. Appl. 59, (2010), 3458-3463.
Sezgin, A., Atagün, A.O. and Aygün, E., A note on soft near-rings and idealistic soft near-rings, Filomat 25, (2011), 53-68.
Majumdar, P. and Samanta, S.K., On soft mappings, Comput. Math. Appl. 60, (9), (2010), 2666-2672.
Karaaslan, F., Cagman, N. and Enginoglu, S., Soft Lattices, Journal of New Results in Science 1 (2012) 5-17.
Atagün, A.O. and Sezgin, A., Soft substructures of rings, fields and modules, Comput. Math. Appl. 61(3), (2011), 592-601.
Çağman, N., Çıtak, F., Aktaş, H., Soft int-group and its applications to group theory, Neural Comput. Appl. 21, (Issue 1-Supplement), (2012), 151-158.
A. Sezgin,N. Çağman, Z. Kaya Türk , E. Muştuoğlu, Soft uni-groups and its applications to group theory, submitted.
E. Muştuoğlu, A. Sezgin, Z. Kaya Türk, Some characterizations on soft uni-groups and normal soft uni-groups, International Journal of Computer Applications 155, 2016.

Yıl 2019, Cilt: 68 Sayı: 1, 334 - 352, 01.02.2019

Aslıhan Sezgin Naim Çağman Filiz Çıtak

https://doi.org/10.31801/cfsuasmas.420457

Cited By: 14

Öz

Kaynakça

Molodtsov, D., Soft set theory-first results, Comput. Math. Appl. 37, (1999), 19-31.
Maji, P.K., Biswas R. and Roy, A.R., Soft set theory, Comput. Math. Appl. 45, (2003), 555-562.
Ali, M.I., Feng, F., Liu, X., Min, W.K, and Shabir, M., On some new operations in soft set theory, Comput. Math. Appl. 57, (2009), 1547-1553.
Sezgin A., and Atagün, A.O, On operations of soft sets, Comput. Math. Appl. 61(5), (2011), 1457-1467.
Cağman, N., and Enginoğlu S., Soft matrix theory and its decision making, Comput. Math. Appl. 59, (2010) 3308-3314.
Cağman, N. and Enginoğlu, S. Soft set theory and uni-int decision making, Eur. J. Oper. Res. 207, (2010) 848-855.
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.
Molodtsov, D.A., Yu., V, Leonov and Kovkov, D. V., Soft sets technique and its application, Nechetkie Sistemi i Myakie Vychisleniya 1-1 (2006), 8-39.
Zou, Y. and Xiao, Z., Data analysis approaches of soft sets under incomplete information, Knowledge Based Systems 21, (2008), 941-945.
Zhan, J. Liu, Q., Herawan, T.,A novel soft rough set: soft rough hemirings and its multicriteria group decision making, Applied Soft Computing 54, (2017), 393--402.
Ma, X., Liu, Q., Zhan, J., A survey of decision making methods based on certain hybrid soft set models, Artificial Intelligence Review 47, (2017), 507--530.
Zhan, J., Zhu, K., A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Computing 21, (2017), 1923--1936.
Zhan, J., Ali, M.I, Mehmood, N., On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods, Applied Soft Computing 56, (2017), 446--457.
Aktas, H. and Cağman, N., Soft sets and soft groups, Inform. Sci. 177, (2007), 2726-2735.
Feng, F., Jun, Y.B. and X. Zhao, Soft semirings, Comput. Math. Appl. 56, (2008), 2621-2628.
Jun, Y.B., Soft BCK/BCI-algebras, Comput. Math. Appl. 56, (2008), 1408-1413.
Jun, Y.B and Park, C.H., Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci. 178, (2008), 2466-2475.
Jun, Y.B., Lee, K.J. and Zhan, J. Soft p-ideals of soft BCI-algebras, Comput. Math. Appl. 58, (2009), 2060-2068.
Kazancı, O., Yılmaz, S. and Yamak, S., Soft sets and soft BCH-algebras, Hacet. J. Math. Stat. 39, (2), (2010), 205-217.
Acar, U., Koyuncu, F. and Tanay, B., Soft sets and soft rings, Comput. Math. Appl. 59, (2010), 3458-3463.
Sezgin, A., Atagün, A.O. and Aygün, E., A note on soft near-rings and idealistic soft near-rings, Filomat 25, (2011), 53-68.
Majumdar, P. and Samanta, S.K., On soft mappings, Comput. Math. Appl. 60, (9), (2010), 2666-2672.
Karaaslan, F., Cagman, N. and Enginoglu, S., Soft Lattices, Journal of New Results in Science 1 (2012) 5-17.
Atagün, A.O. and Sezgin, A., Soft substructures of rings, fields and modules, Comput. Math. Appl. 61(3), (2011), 592-601.
Çağman, N., Çıtak, F., Aktaş, H., Soft int-group and its applications to group theory, Neural Comput. Appl. 21, (Issue 1-Supplement), (2012), 151-158.
A. Sezgin,N. Çağman, Z. Kaya Türk , E. Muştuoğlu, Soft uni-groups and its applications to group theory, submitted.
E. Muştuoğlu, A. Sezgin, Z. Kaya Türk, Some characterizations on soft uni-groups and normal soft uni-groups, International Journal of Computer Applications 155, 2016.

Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Makaleler
Yazarlar	Aslıhan Sezgin 0000-0002-1519-7294 Naim Çağman 0000-0003-3037-1868 Filiz Çıtak 0000-0003-1784-1845
Yayımlanma Tarihi	1 Şubat 2019
Gönderilme Tarihi	16 Kasım 2017
Kabul Tarihi	16 Ocak 208
Yayımlandığı Sayı	Yıl 2019 Cilt: 68 Sayı: 1

Kaynak Göster

APA	Sezgin, A., Çağman, N., & Çıtak, F. (2019). α-inclusions applied to group theory via soft set and logic. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 334-352. https://doi.org/10.31801/cfsuasmas.420457
AMA	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. Şubat 2019;68(1):334-352. doi:10.31801/cfsuasmas.420457
Chicago	Sezgin, Aslıhan, Naim Çağman, ve Filiz Çıtak. “α-Inclusions Applied to Group Theory via Soft Set and Logic”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 1 (Şubat 2019): 334-52. https://doi.org/10.31801/cfsuasmas.420457.
EndNote	Sezgin A, Çağman N, Çıtak F (01 Şubat 2019) α-inclusions applied to group theory via soft set and logic. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 334–352.
IEEE	A. Sezgin, N. Çağman, ve F. Çıtak, “α-inclusions applied to group theory via soft set and logic”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 334–352, 2019, doi: 10.31801/cfsuasmas.420457.
ISNAD	Sezgin, Aslıhan vd. “α-Inclusions Applied to Group Theory via Soft Set and Logic”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (Şubat 2019), 334-352. https://doi.org/10.31801/cfsuasmas.420457.
JAMA	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. 2019;68:334–352.
MLA	Sezgin, Aslıhan vd. “α-Inclusions Applied to Group Theory via Soft Set and Logic”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 1, 2019, ss. 334-52, doi:10.31801/cfsuasmas.420457.
Vancouver	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. 2019;68(1):334-52.