Soft covered ideals in semigroups

Şerif Özlü; Aslıhan Sezgin

doi:10.2478/ausm-2020-0023

Abstract

In this work, soft covered ideals in semigroups are constructed and in this concept, soft covered semigroups, soft covered left (right) ideals, soft covered interior ideals, soft covered (generalized) bi-ideals and soft covered quasi ideals of a semigroup are defined. Various properties of these ideals are introduced and the interrelations of these soft covered ideals and the relations of soft anti covered ideals and soft covered ideals are investigated.

References

[1] D. Molodtsov, Soft set theory-first results, Comput Math Appl., 37 (1999), 19–31.10.1016/S0898-1221(99)00056-5
Search in Google Scholar Back to article
[2] H. Aktaṣ and N. ̣Cağman, Soft sets and soft groups, Inform Sci., 177 (2007), 2726–2735.10.1016/j.ins.2006.12.008
Search in Google Scholar Back to article
[3] F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Comput Math Appl., 56 (2008), 2621–2628.10.1016/j.camwa.2008.05.011
Search in Google Scholar Back to article
[4] U. Acar, F. Koyuncu and B. Tanay, Soft sets and soft rings, Comput Math Appl, 59 (2010), 3458–3463.10.1016/j.camwa.2010.03.034
Search in Google Scholar Back to article
[5] Y. B. Jun, Soft BCK/BCI-algebras, Comput Math Appl., 56 (2008), 1408– 1413.10.1016/j.camwa.2008.02.035
Search in Google Scholar Back to article
[6] Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform Sci., 178 (2008), 2466–2475.
Search in Google Scholar Back to article
[7] Y. B. Jun, K. J. Lee and J. Zhan, Soft p-ideals of soft BCI-algebras, Comput Math Appl., 58 2009, 2060–2068.10.1016/j.camwa.2009.07.072
Search in Google Scholar Back to article
[8] Y. B. Jun, K. J. Lee, C. H. Park, Soft set theory applied to ideals in d-algebras, Comput. Math. Appl., 57 (3) (2009), 367–378.
Search in Google Scholar Back to article
[9] J. Zhan, Y. B. Jun, Soft BL-algebras based on fuzzy sets, Comput Math Appl., 59 (6) (2010), 2037–2046.
Search in Google Scholar Back to article
[10] O. Kazancı, Ş. Yılmaz and S. Yamak, Soft sets and soft BCH-algebras, Hacet J Math Stat., 39 (2) (2010), 205–217.
Search in Google Scholar Back to article
[11] A. Sezgin and A. O. Atagün and E. Aygün, A note on soft N-groups and idealistic soft N-groups, Filomat, 25 (1), 53–68.10.2298/FIL1101053S
Search in Google Scholar Back to article
[12] N. ̣Cağman and S. Enginoğlu, Soft matrix theory and its decision making, Comput Math Appl., 59 (2010), 3308–3314.10.1016/j.camwa.2010.03.015
Search in Google Scholar Back to article
[13] N. ̣Cağman and S. Enginoğlu, Soft set theory and uni-int decision making, Eur J Oper Res., 207 (2010), 848–855.10.1016/j.ejor.2010.05.004
Search in Google Scholar Back to article
[14] P. K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making problem, Comput Math Appl., 44 (2002), 1077–1083.10.1016/S0898-1221(02)00216-X
Search in Google Scholar Back to article
[15] Y. Zou and Z. Xiao, Data analysis approaches of soft sets under incomplete information, Knowled-Based Syst., 21 (2008), 941–945.10.1016/j.knosys.2008.04.004
Search in Google Scholar Back to article
[16] D. Mandal, Fuzzy ideals and fuzzy interior idelas in ordered semigroups, In Fuzzy Information and Engineering, (2014), 101–114.10.1016/j.fiae.2014.06.008
Search in Google Scholar Back to article
[17] K. A. Dib and N. Galhum, Fuzzy ideals and fuzzy bi-ideals in fuzzy semi-groups, Fuzzy Sets and Systems, 92 (1992), 103–111.10.1016/S0165-0114(96)00170-4
Search in Google Scholar Back to article
[18] O. Kazancý and S. Yamak, Generalized fuzzy bi-ideals of semigroup, Soft Computing, 12 (2008), 1119–1124.10.1007/s00500-008-0280-5
Search in Google Scholar Back to article
[19] J. Kavikumar, A. B. Khamis, Fuzzy Ideals and Fuzzy Quasi-ideals in Ternary Semirings, IAENG International Journal of Applied Mathematics, 37 (2) (2007).
Search in Google Scholar Back to article
[20] T. Changphas and P. Summaprab, On Ordered Semigroups Containing Covered Ideals, Communications in Algebra, 44 (9) (2016), 4104–4113, DOI: 10.1080/00927872.2015.1087015.10.1080/00927872.2015.1087015
Search in Google Scholar Back to article
[21] A. S. Sezgin, N. ̣Cağman, A. O. Atagün, M. I. Ali, Türkmen E. Soft intersection semigroups, ideals and bi-ideals; a new application on semigroup theory I, Filomat, 29 (5) (2015), 917–946.10.2298/FIL1505917S
Search in Google Scholar Back to article
[22] A. S. Sezgin, N. ̣Cağman, A. O. Atagün, Soft intersection interior ideals, quasi-ideals and generalized bi-ideals; a new approach to semigroup theory II, Journal of Multiple-Valued Logic and Soft Computing, 23 (1–2) (2014), 161–207.
Search in Google Scholar Back to article
[23] I. Fabrici, Semigroups containing covered one-sided ideals, Mahematica Slovaca, 31 (1981), 225–231.
Search in Google Scholar Back to article
[24] I. Fabrici, Semigroups containing covered two-sided ideals, Mahematica Slovaca, 34 (1984), 355–363.
Search in Google Scholar Back to article
[25] X., Xie, F. Yan, Fuzzy Anti-Covered Left Ideals in Semigroups, submitted.
Search in Google Scholar Back to article
[26] A. Sezgin, Ş Özlü, Soft Anti-Covered Ideals in Semigroups, submitted.
Search in Google Scholar Back to article
[27] N. Çağman, F. Çıtak and H. Aktaş, Soft int-groups and its applications to group theory, Neural Comput. Appl., 21 (1) (2012), 151–158.10.1007/s00521-011-0752-x
Search in Google Scholar Back to article

Soft covered ideals in semigroups

Abstract

Paradigm

My account