Intersection soft ideals and their quotients on KU-algebras

Moin A. Ansari; Ali N. A. Koam; Azeem Haider; Moin A. Ansari; Ali N. A. Koam; Azeem Haider

doi:10.3934/math.2021700

AIMS Mathematics

2021, Volume 6, Issue 11: 12077-12084. doi: 10.3934/math.2021700

Previous Article Next Article

Research article Special Issues

Intersection soft ideals and their quotients on KU-algebras

Department of Mathematics, College of Science, Jazan University, Jazan, Saudi Arabia

Received: 28 May 2021 Accepted: 12 August 2021 Published: 19 August 2021
MSC : 06F35, 03G25

In this paper, we have discussed quotient structures of KU-algebras by using the concept of intersection soft ideals. In general, the soft sets are parameterized families of sets that are used to dealt with uncertainty. In particular, We have given the fundamental homomorphism theorem of quotient KU-algebras. A characterization of commutative quotient KU-algebras, implicative quotient KU-algebras and positive implicative quotient KU-algebras are also presented.
- KU-algebras,
- soft sets,
- intersection soft ideals,
- quotient KU-algebras
Citation: Moin A. Ansari, Ali N. A. Koam, Azeem Haider. Intersection soft ideals and their quotients on KU-algebras[J]. AIMS Mathematics, 2021, 6(11): 12077-12084. doi: 10.3934/math.2021700

Related Papers:

Abstract

In this paper, we have discussed quotient structures of KU-algebras by using the concept of intersection soft ideals. In general, the soft sets are parameterized families of sets that are used to dealt with uncertainty. In particular, We have given the fundamental homomorphism theorem of quotient KU-algebras. A characterization of commutative quotient KU-algebras, implicative quotient KU-algebras and positive implicative quotient KU-algebras are also presented.

References

[1]	A. N. A. Koam, A. Haider, M. A. Ansari, Pseudo-metric on KU-algebras, Korean J. Math., 27 (2019), 131–140.
[2]	A. N. A. Koam, M. A. Ansari, A, Haider, n-ary block codes related to KU-algebras, J. Taibah Univ. Sci., 14 (2020), 172–176. doi: 10.1080/16583655.2020.1713585
[3]	A. N. A. Koam, A. Haider, M. A. Ansari, On an extension of KU-algebras, AIMS Math., 6 (2020), 1249–1257.
[4]	F. Feng, Soft rough sets applied to multicriteria group decision making, Ann. Fuzzy Math. Inform., 2 (2011), 69–80.
[5]	Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl., 56 (2008), 1408–1413.
[6]	F. Feng, Y. Li, Soft subsets and soft product operations, Inform. Sciences, 232 (2013), 44–57. doi: 10.1016/j.ins.2013.01.001
[7]	G. Muhiuddin, Intersectional soft sets theory applied to generalized hypervector spaces, An. Sti. U. Ovid. Co-Mat., 28 (2020), 171–191.
[8]	G. Muhiuddin, A. Mahboob, Int-soft ideals over the soft sets in ordered semigroups, AIMS Math., 5 (2020), 2412–2423. doi: 10.3934/math.2020318
[9]	F. Feng, Z. Xu, H. Fujita, M. Liang, Enhancing PROMETHEE method with intuitionistic fuzzy soft sets, Int. J. Intell. Syst., 35 (2020), 1071–1104. doi: 10.1002/int.22235
[10]	Y. B. Jun, Commutative intersection-soft ideals in BCK-algebras, J. Mult.-Valued Logic Soft Comput., 21 (2013), 525–539.
[11]	M. A. Ansari, A. N. A. Koam, Rough approximations in KU-algebras, Italian J. Pure Appl. Math., 40 (2018), 679–691.
[12]	M. A. Ansari, A. N. A. Koam, A. Haider, On KU-algebras containing $(\alpha, \beta)$-US soft sets, Korean J. Math., 28 (2020), 89–104.
[13]	D. Molodtsov, Soft set theory first results, Comput. Math. Appl., 37 (1999), 19–31.
[14]	N. Yaqoob, S. M. Mostafa, M. A. Ansari, On cubic KU-ideals of KU-algebras, Int. Scholarly Res. Not., 2013 (2013), 935905.
[15]	C. Prabpayak, U. Leerawat, On ideals and congruences in KU-algebras, Sci. Magna J., 5 (2009), 54–57.
[16]	C. Prabpayak, U. Leerawat, On isomorphisms of KU-algebras, Sci. Magna J., 5 (2009), 25–31.
[17]	S. M. Mostafa, M. A. Abd-Elnaby, M. M. M. Yousef, Fuzzy ideals of KU-algebras, Int. Math. Forum, 6 (2011), 3139–3149.
[18]	S. Yuksel, T. Dizman, G. Yildizdan, U. Sert, Application of soft sets to diagnose the prostate cancer risk, J. Inequal. Appl., 2013 (2013), 1–11. doi: 10.1186/1029-242X-2013-1
[19]	P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl., 45, (2003), 555–562.
[20]	X. Ma, J. Zhan, Y. Xu, Lattice implication algebras based on soft set theory, In: World scientific proceedings series on computer engineering and information science, Computational Intelligence, 2010,535–540.
[21]	M. Akram, G. Ali, J. C. R. Alcantud, F. Fatimah, Parameter reductions in N-soft sets and their applications in decision-making, Expert Syst., 38 (2021), e12601.
[22]	R. A. Borzooei, E. Babaei, Y. B. Jun, M. A. Kologani, M. M. Takallo, Soft set theory applied to hoops, An. Sti. U. Ovid. Co-Mat., 28 (2020), 61–79.

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)