Research article Special Issues

Intersection soft ideals and their quotients on KU-algebras

  • 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.

    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:

  • 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.



    加载中


    [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
  • © 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(1722) PDF downloads(109) Cited by(1)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog