Original Research Article

Article volume = 2022 and issue = 1

Pages: 79–89

Article publication Date: November 21, 2022

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# Q-soft cosets, characteristic Q-soft and Q-level subsets of Q-soft subgroups

#### Rasul Rasuli

Department of Mathematics, Payame Noor University(PNU), P. O. Box 19395-4697, Tehran, Iran.

##### Abstract:

In this paper, we introduce the concept $Q$-soft coset and $Q$-soft middle coset of group $G$ and investigate some of their properties and structured characteristics. Next we define characteristic $Q$-soft subgroup and generalized characteristic $Q$-soft subgroup of groups and obtain some resuls about them. Finally, we introduce $Q$-level subgroups of $Q$-soft subgroups and investigate some of their properties.

##### Keywords:

Q-soft subsets, Group theory, Q-soft subgroups, Q-soft normal subgroups, Homomorphism, Q-soft cosets, Q-level subsets.

##### References:

- [1] H. Aktas and N. Cagman, Soft sets and soft groups, Inform. Sci., 177(2007), 2726-2735. 1
- [2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96. 1
- [3] K. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64 (1994), 159-174. 1
- [4] W. L. Gau and D. J. Buehrer, Vague sets, IEEE Trans. System Man Cybernet, 23 (1993), 610-614. 1
- [5] M. B. Gorzalzany, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems , 21 (1987), 1-17. 1
- [6] F. Hassani and R. Rasuli, Q-soft Subgroups and Anti-Q-soft Subgroups in Universal Algebra, The Journal of Fuzzy Mathematics Los Angeles 26 (1) (2018), 139-152. 1, 2.10, 2.12, 2.13, 2.14
- [7] T. Hungerford, Algebra, Graduate Texts in Mathematics. Springer (2003). 2.1, 2.4, 2.5, 2.6
- [8] P. K. Maji, R. Biswas and A. R. Roy, Sof tset theory, Computer Mathematics with Applications, 45 (2003), 555-562. 2.7, 2.8
- [9] D. A. Molodtsov, Soft set theory-First results, Computers & Mathematics With Applications 37 (4) (1999), 19-31. 1, 2.7, 2.8
- [10] Z. Pawlak, Rough sets, International Journal of Information and Computer Sciences , 11 (1982), 341-356. 1
- [11] Z. Pawlak, Hard set and soft sets, ICS Research Report, Institute of Computer Sczence, Poland, (1994). 1
- [12] R. Rasuli, Extension of Q-soft ideals in semigroups, Int. J. Open Problems Compt. Math., 10 (2) (2017), 6-13. 1
- [13] R. Rasuli, Soft Lie Ideals and Anti Soft Lie Ideals, The Journal of Fuzzy Mathematics Los Angeles 26 (1) (2018),193-202. 1
- [14] R. Rasuli, Q-Soft Normal Subgroups, Journal of New Theory 26 (2019), 13-22. 1, 2.15, 2.16, 4, 4
- [15] R. Rasuli, Anti Q-soft Normal Subgroups, The Journal of Fuzzy Mathematics Los Angles 28 (2020), 237-248. 1
- [16] R. Rasuli, Characterization of Q-soft R-submodules over commutative rings, The Second National Congress on Mathematics and Statistics Conbad Kavous University, 2020. 1
- [17] R. Rasuli and M. M. Moatamedi nezhad, Anti Q-soft R-submodules, The First National Conference on Soft Computing and Cognitive Science Conbad Kavous University, July 2020. 1
- [18] A. Rosenfeld, fuzzy groups, J. math. Anal. Appl., 35(1971), 512-517. 1
- [19] A. Solairaju and R. Nagarajan, Q- fuzzy left R- subgroups of near rings w.r.t T- norms, Antarctica journal of mathematics, 5(2008), 51-57. 1
- [20] A. Solairaju and R. Nagarajan, A New Structure and Construction of Q-Fuzzy Groups, Advances in Fuzzy mathematics, 4(2009), 23-29. 1
- [21] X. Yin and Z. Liao, Study on Soft Groups, Journal of Computers, 8(2013), 960-967. 1
- [22] L. A. Zadeh, Fuzzy sets, Infor. and Control, 8 (1965), 338-353. 1

##### Cite this article as:

- Rasul Rasuli, Q-soft cosets, characteristic Q-soft and Q-level subsets of Q-soft subgroups, Communications in Combinatorics, Cryptography & Computer Science, 2022(1), PP.79–89, 2022
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