Positive Implicative Hyper BCK-Ideals of Hyper BCK-Algebras Under an Interval-Valued Intuitionistic Fuzzy Environment

Main Article Content

D. Ramesh, R. Durga Prasad, Sheke Baji, Aiyared Iampan, B. Satyanarayana

Abstract

This paper contains some new theorems related to hyper BCK-ideals positive implicative hyper BCK-ideals of types-1, 2, 3, 4 of hyper BCK-algebras (HBCKA) under an interval-valued intuitionistic fuzzy environment. Henceforth, the connection between these ideas and their relevant characteristics is discussed.

Article Details

References

  1. K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3.
  2. K.T. Atanassov, Intuitionistic Fuzzy Sets, Physica-Verlag, Heidelberg, 1999. https://doi.org/10.1007/978-3-7908-1870-3.
  3. K.T. Atanassov, New Operations Defined over the Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 61 (1994), 137–142. https://doi.org/10.1016/0165-0114(94)90229-1.
  4. K. Atanassov, G. Gargov, Interval Valued Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 31 (1989), 343–349. https://doi.org/10.1016/0165-0114(89)90205-4.
  5. M. Bakhshi, R.A. Borzooei, M.M. Zahedi, Fuzzy (Positive, Weak) Implicative Hyper BCK-Ideals, Iran. J. Fuzzy Syst. 1 (2004), 63-79. https://doi.org/10.22111/ijfs.2004.506.
  6. R.A. Borzooei, M. Bakhshi, Some Results on Hyper BCK-Algebras, Quasigroups Related Syst. 11 (2004), 9-24.
  7. R.A. Borzooei, M. Bakhshi, (Weak) Implicative Hyper BCK-Ideals, Quasigroups Related Syst. 12 (2004), 13-28.
  8. R.A. Borzooei, P. Corsini, M.M. Zahedi, Some Kinds of Positive Implicative Hyper K-Ideals, J. Discrete Math. Sci. Cryptogr. 6 (2003), 97–108. https://doi.org/10.1080/09720529.2003.10697966.
  9. R.A. Borzooei, Y.B. Jun, Intuitionistic Fuzzy Hyper BCK-Ideals of Hyper BCK-Algebras, Iran. J. Fuzzy Syst. 1 (2004), 65-77. https://doi.org/10.22111/ijfs.2004.495.
  10. R.A. Borzooei, M.M. Zahedi, H. Rezaei, Classification of Hyper Bck-Algebras of Order 3, Italian J. Pure Appl. Math. 12 (2002), 175-184.
  11. Y. Imai, K. Iséki, On Axiom Systems of Propositional Calculi, XIV, Proc. Japan Acad., Ser. A, Math. Sci. 42 (1966), 19-22. https://doi.org/10.3792/pja/1195522169.
  12. Y.B. Jun, M.M. Zahedi, X.L. Xin, R.A. Borzooei, On Hyper BCK-Algebra, Italian J. Pure Appl. Math. 8 (2000), 127-136.
  13. F. Marty, Sur une Généralisation de la Notion de Groupe, in: 8th Congress Mathematics, Scandinaves, Stockholm, (1934), 45-49. https://api.semanticscholar.org/CorpusID:222416358.
  14. D. Ramesh, M.S. Kumar, N. Srimannarayana, D. Devanandam, B. Satyanarayana, Results on Quotient BF-Algebras via Interval-Valued Fuzzy Dual Ideals, Int. J. Adv. Sci. Technol. 29 (2020), 1193-1197.
  15. D. Ramesh, K.K. Rao, R.D. Prasad, N. Srimannarayana, B. Satyanarayana, Translations of Intuitionistic Fuzzy Subalgebras in BF-Algebras, Adv. Math.: Sci. J. 9 (2020), 8837–8844. https://doi.org/10.37418/amsj.9.10.107.
  16. D. Ramesh, B. Satyanarayana, N. Srimannarayana, Direct Product of Finite Interval-Valued Intuitionistic Fuzzy Ideals in BF-Algebra, Int. J. Eng. Technol. 7 (2018), 631–635. https://doi.org/10.14419/ijet.v7i3.34.19404.
  17. D. Ramesh, B. Satyanarayana, N. Srimannarayana, On Quotient BF-Algebras via Interval-Valued Intuitionistic Fuzzy Ideals, J. Anal. 27 (2019), 151–160. https://doi.org/10.1007/s41478-018-0111-8.
  18. B. Satyanarayana, L. Krishna, R.D. Prasad, On Interval-Valued Intuitionistic Fuzzy Hyper BCK-Ideals of Hyper BCK-Algebras, J. Adv. Math. 7 (2014), 1219-1226.
  19. B. Satyanarayana, K.V.P. Veneela, R.D. Prasad, U.B. Madhavi, Interval-Valued Intuitionistic Fuzzy Positive Implicative Hyper BCK-Ideal of Hyper BCK-Algebras, Adv. Appl. Sci. Res. 7 (2016), 32-40. https://api.semanticscholar.org/CorpusID:32152154.
  20. L.A. Zadeh, Fuzzy Sets, Inf. Control 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X.