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Cubic intuitionistic structure of KU-algebras

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Abstract

In this paper, the notions of cubic intuitionistic KU-subalgebras and KU-ideals of a KU-algebras are introduced, and several properties are investigated. Characterizations of cubic intuitionistic KU-subalgebras and KU-ideals of KU-algebras are considered. Relations between a cubic intuitionistic KU-subalgebra and a cubic intuitionistic KU-ideal are given.

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References

  1. Akram, M., Yaqoob, N., Kavikumar, J.: Interval valued \((\tilde{\theta }, \tilde{\delta })\)-fuzzy \(KU\)-ideals of \(KU\)-algebras. Int. J. Pure Appl. Math. 92(3), 335–349 (2014)

    Article  Google Scholar 

  2. Akram, M., Yaqoob, N., Gulistan, M.: Cubic \(KU\)-subalgebras. Int. J. Pure Appl. Math. 89(5), 659–665 (2013)

    Google Scholar 

  3. Gulistan, M., Shahzad, M., Ahmed, S.: On \((\alpha,\beta )\)-fuzzy \(KU\)-ideals of \(KU\)-algebras. Afr. Mat. 26(3–4), 651–661 (2015)

    Article  MathSciNet  Google Scholar 

  4. Gulistan, M., Shahzad, M., Yaqoob, N.: On \((\in,\in \vee Q_{K})\)-fuzzy \(KU\)-ideals of \(KU\)-algebras. Acta Universitatis Apulensis 39, 75–83 (2014)

    Article  Google Scholar 

  5. Gulistan, M., Shahzad, M.: On soft \(KU\)-algebras. J. Algebra Number Theory Adv. Appl. 11(1), 1–20 (2014)

    MATH  Google Scholar 

  6. Gulistan, M., Yaqoob, N., Vougiouklis, T., Wahab, H.Abdul: Extensions of cubic ideals in weak left almost semihypergroups. J. Intell. Fuzzy Syst. 34(6), 4161–4172 (2018)

    Article  Google Scholar 

  7. Jun, Y.B., Kim, C.S., Yang, K.O.: Cubic sets. Ann. Fuzzy Math. Inf. 4, 83–98 (2012)

    MathSciNet  MATH  Google Scholar 

  8. Jun, Y.B., Muhiuddin, G., Ozturk, M.A., Roh, E.H.: Cubic soft ideals in \(BCK/BCI\)-algebras. J. Comput. Anal. Appl. 22, 929–940 (2017)

    MathSciNet  Google Scholar 

  9. Jun, Y.B.: A novel extension of cubic sets and its applications in \(BCK/BCI\)-algebras. Ann. Fuzzy Math. Inf. 14(5), 475–486 (2017)

    Article  MathSciNet  Google Scholar 

  10. Khan, M., Jun, Y.B., Gulistan, M., Yaqoob, N.: The generalized version of Jun’s cubic sets in semigroups. J. Intell. Fuzzy Syst. 28(2), 947–960 (2015)

    Article  MathSciNet  Google Scholar 

  11. Ma, X.L., Zhan, J., Khan, M., Gulistan, M., Yaqoob, N.: Generalized cubic relations in \(H_{v}\)-LA-semigroups. J. Discr. Math. Sci. Cryptogr. 21(3), 607–630 (2018)

    Google Scholar 

  12. Mostafa, S.M., Abd-Elnaby, M.A., Yousef, M.M.: Fuzzy ideals of \(KU\)-algebras. Int. Math. Forum 6(63), 3139–3149 (2011)

    MathSciNet  MATH  Google Scholar 

  13. Mostafa, S.M., Naby, M.A.Abdel, Elgendy, O.R.: Intuitionistic fuzzy \(KU\)-ideals in \(KU\)-algebras. Int. J. Math. Sci. Appl. 1(3), 1379–1384 (2011)

    MathSciNet  MATH  Google Scholar 

  14. Mostafa, S.M., Kareem, F.F.: \(N\)-fold commutative \(KU\)-Algebras. Int. J. Algebra 8(6), 267–275 (2014)

    Article  Google Scholar 

  15. Muhiuddin, G.: Bipolar fuzzy \(KU\)-subalgebras\(\setminus \)ideals of \(KU\)-algebras. Ann. Fuzzy Math. Inf. 8(3), 409–418 (2014)

    MathSciNet  MATH  Google Scholar 

  16. Muhiuddin, G., Al-roqi, A.M.: Cubic soft sets with applications in \(BCK/BCI\)-algebras. Ann. Fuzzy Math. Inf. 8, 291–304 (2014)

    MathSciNet  MATH  Google Scholar 

  17. Muhiuddin, G., Feng, F., Jun, Y.B.: Subalgebras of \(BCK/BCI\)-algebras based on cubic soft sets. Sci. World J. 2014, 9 (2014). Article ID 458638

    Google Scholar 

  18. Prabpyak, C., Leerawat, U.: On ideals and congruences in \(KU\)-algebras. Sci. Magn. 5(1), 54–57 (2009)

    Google Scholar 

  19. Senapati, T.: \(T\)-fuzzy \(KU\)-subalgebras of \(KU\)-algebras. Ann. Fuzzy Math. Inf. 10(2), 261–270 (2015)

    MathSciNet  MATH  Google Scholar 

  20. Senapati, T.: \(T\)-fuzzy \(KU\)-ideals of \(KU\)-algebras. Afr. Mat. 29(3–4), 591–600 (2018)

    Article  MathSciNet  Google Scholar 

  21. Senapati, T., Shum, K.P.: Atanassov’s intuitionistic fuzzy bi-normed \(KU\)-subalgebras of a \(KU\)-algebra. Missouri J. Math. Sci. 29, 92–112 (2017)

    Article  MathSciNet  Google Scholar 

  22. Senapati, T., Shum, K.P.: Atanassov’s intuitionistic fuzzy bi-normed \(KU\)-ideals of a \(KU\)-algebra. J. Intell. Fuzzy Syst. 30, 1169–1180 (2016)

    Article  Google Scholar 

  23. Senapati, T., Kim, C.S., Bhowmik, M., Pal, M.: Cubic subalgebras and cubic closed ideals of \(B\)-algebras. Fuzzy Inf. Eng. 7(2), 129–149 (2015)

    Article  MathSciNet  Google Scholar 

  24. Senapati, T.: Cubic \(BF\)-subalgebras of \(BF\)-algebras. An. Univ. Oradea Fasc. Mat. 23(1), 97–105 (2016)

    MathSciNet  MATH  Google Scholar 

  25. Senapati, T., Jun, Y.B., Shum, K.P.: Cubic set structure applied in \(UP\)-algebras. Discr. Math. Algorithm Appl. 10(4), 1850049 (2018). https://doi.org/10.1142/S1793830918500490

    Article  MathSciNet  MATH  Google Scholar 

  26. Senapati, T., Shum, K.P.: Cubic commutative ideals of \(BCK\)-algebras. Missouri J. Math. Sci. 30(1), 5–19 (2018)

    Article  MathSciNet  Google Scholar 

  27. Senapati, T., Shum, K.P.: Cubic implicative ideals of \(BCK\)-algebras. Missouri J. Math. Sci. 29(2), 125–138 (2017)

    Article  MathSciNet  Google Scholar 

  28. Senapati, T., Jun, Y.B., Muhiuddin, G., Shum, K.P.: Cubic intuitionistic structures applied to ideals of BCI-algebras. An. St. Univ. Ovidius Constanta 25(2), 213–232 (2019)

    MathSciNet  Google Scholar 

  29. Senapati, T., Jana, C., Pal, M., Jun, Y.B.: Cubic Intuitionistic \(q\)-ideals of BCI-algebras. Symmetry 10(12), 752 (2018). https://doi.org/10.3390/sym10120752

    Article  MATH  Google Scholar 

  30. Senapati, T., Jun, Y.B., Shum, K.P.: Cubic intuitionistic subalgebras and closed cubic intuitionistic ideals of B-algebras. J. Intell. Fuzzy Syst. 36(2), 1563–1571 (2019)

    Article  Google Scholar 

  31. Yaqoob, N., Mostafa, S.M., Ansari, M.A.: On cubic \(KU\)-ideals of \(KU\)-algebras. ISRN Algebra Article ID 935905, 10 (2013)

  32. Yaqoob, N., Gulistan, M., Leoreanu-Fotea, V., Hila, K.: Cubic hyperideals in LA-semihypergroups. J. Intell. Fuzzy Syst. 34(4), 2707–2721 (2018)

    Article  Google Scholar 

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Acknowledgements

The authors would like to express sincere appreciation to the referees for their valuable suggestions and comments helpful in improving this paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Beibei, 400715, Chongqing, China

    Tapan Senapati

  2. Department of Mathematics Education, Gyeongsang National University, Jinju, 52828, Korea

    Young Bae Jun

  3. Institute of Mathematics, Yunnan University, Kunming, 650091, China

    K. P. Shum

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  1. Tapan Senapati
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  2. Young Bae Jun
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  3. K. P. Shum
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Correspondence to Tapan Senapati .

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Senapati , T., Jun, Y.B. & Shum, K.P. Cubic intuitionistic structure of KU-algebras. Afr. Mat. 31, 237–248 (2020). https://doi.org/10.1007/s13370-019-00720-0

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