Approximations of quasi and interior hyperfilters in partially ordered LA-semihypergroups

Naveed Yaqoob; Jian Tang; Naveed Yaqoob; Jian Tang

doi:10.3934/math.2021461

AIMS Mathematics

2021, Volume 6, Issue 8: 7944-7960. doi: 10.3934/math.2021461

Previous Article Next Article

Research article

Approximations of quasi and interior hyperfilters in partially ordered LA-semihypergroups

Naveed Yaqoob ^{1
,
,},
Jian Tang ²

1.
Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, Pakistan
2.
School of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui, China

Received: 31 December 2020 Accepted: 11 May 2021 Published: 20 May 2021
MSC : 20N20

In this paper, we define type-1 quasi-hyperfilters (resp., type-1 strong quasi-hyperfilters, type-2 quasi-hyperfilters, type-2 strong quasi-hyperfilters, interior hyperfilters, strong interior hyperfilters, interior semihyperfilters, strong interior semihyperfilters) of an ordered LA-semihypergroup. We applied rough set theory to quasi and interior hyperfilters in ordered LA-semihypergroups.
- LA-semihypergroups,
- ordered LA-semihypergroups,
- quasi-hyperfilter,
- interior hyperfilter,
- rough sets
Citation: Naveed Yaqoob, Jian Tang. Approximations of quasi and interior hyperfilters in partially ordered LA-semihypergroups[J]. AIMS Mathematics, 2021, 6(8): 7944-7960. doi: 10.3934/math.2021461

Related Papers:

Abstract

In this paper, we define type-1 quasi-hyperfilters (resp., type-1 strong quasi-hyperfilters, type-2 quasi-hyperfilters, type-2 strong quasi-hyperfilters, interior hyperfilters, strong interior hyperfilters, interior semihyperfilters, strong interior semihyperfilters) of an ordered LA-semihypergroup. We applied rough set theory to quasi and interior hyperfilters in ordered LA-semihypergroups.

References

[1]	F. Marty, Sur une generalization de la notion de group, 8th Congres Math. Scandinaves, 1934, 45–49.
[2]	P. Corsini, V. Leoreanu-Fotea, Applications of hyperstructure theory, Springer Science & Business Media, 2003.
[3]	T. Vougiouklis, Hyperstructures and their representations, Hadronic Press, 1994.
[4]	B. Davvaz, I. Cristea, Fuzzy algebraic hyperstructures, In: Studies in Fuzziness and Soft Computing, Springer, Cham, 2015.
[5]	K. Hila, J. Dine, On hyperideals in left almost semihypergroups, ISRN Algebra, 2011 (2011), 1–8.
[6]	N. Yaqoob, P. Corsini, F. Yousafzai, On intra-regular left almost semihypergroups with pure left identity, J. Math., 2013 (2013), 1–10.
[7]	M. A. Kazim, M. Naseeruddin, On almost semigroups, Port. Math., 36 (1977), 41–47.
[8]	N. Yaqoob, M. Gulistan, Partially ordered left almost semihypergroups, J. Egypt. Math. Soc., 23 (2015), 231–235. doi: 10.1016/j.joems.2014.05.012
[9]	I. Rehman, N. Yaqoob, S. Nawaz, Hyperideals and hypersystems in LA-hyperrings, Songklanakarin J. Sci. Technol., 39 (2017), 651–657.
[10]	S. Nawaz, M. Gulistan, S. Khan, Weak LA-hypergroups; neutrosophy, enumeration and redox reaction, Neutrosophic Sets and Systems, 36 (2020), 352–368.
[11]	M. Hu, F. Smarandache, X. Zhang, On neutrosophic extended triplet LA-hypergroups and strong pure LA-semihypergroups, Symmetry, 12 (2020), 1–22.
[12]	N. Yaqoob, I. Cristea, M. Gulistan, S. Nawaz, Left almost polygroups, Ital. J. Pure Appl. Math., 39 (2018), 465–474.
[13]	N. Yaqoob, Approximations in left almost polygroups, J. Intell. Fuzzy Syst., 36 (2019), 517–526. doi: 10.3233/JIFS-18776
[14]	C. Jirojkul, R. Chinram, Fuzzy quasi-ideal subsets and fuzzy quasi-filters of ordered semigroup, Int. J. Pure Appl. Math., 52 (2009), 611–617.
[15]	J. Jakubík, On filters of ordered semigroups, Czech. Math. J., 43 (1993), 519–522. doi: 10.21136/CMJ.1993.128415
[16]	K. Hila, Filters in ordered $\Gamma $-semigroups, Rocky Mt. J. Math., 41 (2011), 189–203.
[17]	N. Kehayopulu, On filters generated in poe-semigroups, Math. Japon., 35 (1990), 789–796.
[18]	X. M. Ren, J. Z. Yan, K. P. Shum, Principal filters of po-semigroups, Pure Math. Appl., 16 (2005), 37–42.
[19]	J. Tang, B. Davvaz, Y. Luo, Hyperfilters and fuzzy hyperfilters of ordered semihypergroups, J. Intell. Fuzzy Syst., 29 (2015), 75–84. doi: 10.3233/IFS-151571
[20]	Z. Pawlak, Rough sets, International Journal of Computer & Information Sciences, 11 (1982), 341–356.
[21]	R. Biswas, S. Nanda, Rough groups and rough subgroups, Bull. Pol. Acad. Sci. Math., 42 (1994), 251–254.
[22]	M. A. Abd-Allah, K. El-Saady, A. Ghareeb, Rough intuitionistic fuzzy subgroup, Chaos Soliton. Fract., 42 (2009), 2145–2153. doi: 10.1016/j.chaos.2009.03.199
[23]	Y. B. Jun, Roughness of gamma-subsemigroups/ideals in gamma-semigroups, B. Korean Math. Soc., 40 (2003), 531–536. doi: 10.4134/BKMS.2003.40.3.531
[24]	M. Shabir, S. Irshad, Roughness in ordered semigroups, World Appl. Sci. J., 22 (2013), 84–105.
[25]	R. Ameri, S. A. Arabi, H. Hedayati, Approximations in (bi-)hyperideals of semihypergroups, IJST, 37 (2013), 527–532.
[26]	S.M. Anvariyeh, S. Mirvakili, B. Davvaz, Pawlak's approximations in $\Gamma $-semihypergroups, Comput. Math. Appl., 60 (2010), 45–53. doi: 10.1016/j.camwa.2010.04.028
[27]	N. Yaqoob, M. Aslam, Generalized rough approximations in $ \Gamma $-semihypergroups, J. Intell. Fuzzy Syst., 27 (2014), 2445–2452. doi: 10.3233/IFS-141214
[28]	N. Yaqoob, M. Aslam, K. Hila, B. Davvaz, Rough prime bi-$ \Gamma $-hyperideals and fuzzy prime bi-$\Gamma $-hyperideals of $\Gamma $ -semihypergroups, Filomat, 31 (2017) 4167–4183.
[29]	B. Davvaz, Approximations in hyperring, J. Mult. Valued Log. S., 15 (2009), 471–488.
[30]	S.O. Dehkordi, B. Davvaz, $\Gamma $-semihyperrings: approximations and rough ideals, B. Malays. Math. Sci. So., 35 (2012), 1035–1047.
[31]	P. He, X. Xin, J. Zhan, On rough hyperideals in hyperlattices, J. Appl. Math., 2013 (2013), 1–10.
[32]	V. Leoreanu-Fotea, The lower and upper approximations in a hypergroup, Inform. Sciences, 178 (2008), 3605–3615. doi: 10.1016/j.ins.2008.05.009
[33]	S. M. Qurashi, M. Shabir, Generalized rough fuzzy ideals in quantales, Discrete Dyn. Nat. Soc., 2018 (2018), 1–11.
[34]	S. M. Qurashi, M. Shabir, Roughness in quantale modules, J. Intell. Fuzzy Syst., 35 (2018), 2359–2372. doi: 10.3233/JIFS-17886
[35]	J. Zhan, N. Yaqoob, M. Khan, Roughness in non-associative po-semihypergroups based on pseudohyperorder relations, J. Mult. Valued Log. S., 28 (2017), 153–177.
[36]	S. S. Ahn, C. Kim, Rough set theory applied to fuzzy filters in BE-algebras, Commun. Korean Math. Soc., 31 (2016), 451–460. doi: 10.4134/CKMS.c150168
[37]	M. I. Ali, T. Mahmood, A. Hussain, A study of generalized roughness in $(\in, \in \vee q_{k})$-fuzzy filters of ordered semigroups, J. Taibah Univ. Sci., 12 (2018), 163–172. doi: 10.1080/16583655.2018.1451067
[38]	T. Mahmood, M. I. Ali, A. Hussain, Generalized roughness in fuzzy filters and fuzzy ideals with thresholds in ordered semigroups, Comput. Appl. Math., 37 (2018), 5013–5033. doi: 10.1007/s40314-018-0615-5
[39]	S. Rasouli, B. Davvaz, Rough filters based on residuated lattices, Knowl. Inf. Syst., 58 (2019), 399–424. doi: 10.1007/s10115-018-1219-5
[40]	L. Torkzadeh, S. Ghorbani, Rough filters in BL-Algebras, Int. J. Math. Math. Sci., 2011 (2011), 1–13.
[41]	F. Bouaziz, N. Yaqoob, Rough hyperfilters in po-LA-semihypergroups, Discrete Dyn. Nat. Soc., 2019 (2019), 1–8.

Reader Comments

Your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)