New types of bipolar fuzzy ideals of BCK-algebras

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G. Muhiuddin, D. Al-Kadi, A. Mahboob, K.P. Shum, New types of bipolar fuzzy ideals of BCK-algebras, Int. J. Anal. Appl., 18 (5) (2020), 859-875.

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G. Muhiuddin, D. Al-Kadi, A. Mahboob, K.P. Shum

Abstract

The notions of bipolar fuzzy closed, bipolar fuzzy positive implicative, bipolar fuzzy implicative ideals of BCK-algebras are introduced, and related properties are investigated. Characterizations of a closed, bipolar fuzzy positive implicative, bipolar fuzzy implicative ideals of BCK-algebras are given, and several properties are discussed. Finally, we prove that if T is an implicative BCK-algebra, then a fuzzy subset µ of T is a bipolar fuzzy ideal of T if and only if it is a bipolar fuzzy implicative ideal of T.

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References

  1. D. Al-Kadi, G. Muhiuddin, Bipolar fuzzy BCI-implicative ideals of BCI-algebras, Ann. Commun. Math. 3 (1) (2020), 88-96.
  2. A. Al-Masarwah, A.G. Ahmad, On some properties of doubt bipolar fuzzy H-ideals in BCK/BCI-algebras, Eur. J. Pure Appl. Math. 11 (2018), 652-670.
  3. Anas Al-masarwah, Abd Ghafur Ahmad, G. Muhiuddin, Doubt N-ideals theory in BCK-algebras based on N-structures, Ann. Commun. Math. 3 (1) (2020), 54-62.
  4. A.M. Al-roqi, G. Muhiuddin, S. Aldhafeeri, Normal Unisoft Filters in R0-algebras. Cogent Math. 4 (2017), 1383006.
  5. J. Chen, S. Li, S. Ma, X. Wang, m-polar fuzzy sets: An extension of bipolar fuzzy sets, Sci. World J. 2014 (2014), Article Id 416530.
  6. P.A. Ejegwa, J. A. Otuwe, Frattini fuzzy subgroups of fuzzy groups Ann. Commun. Math. 2 (1) (2019), 24-31
  7. K. Hayat, T. Mahmood, B.Y. Cao, On bipolar anti fuzzy H-ideals in hemirings, Fuzzy Inf. Eng. 9 (2017), 1-19.
  8. M. Ibrara, A. Khana, B. Davvazb, Characterizations of regular ordered semigroups in terms of (α, β)-bipolar fuzzy generalized bi-ideals, J. Intell. Fuzzy Syst. 33 (2017), 365-376.
  9. Y. Imai, K. Iseki, On axiom systems of propositional calculi, Proc. Japan Acad. 42 (1966), 19-22.
  10. K. Is ´eki, An algebra related with a propositional calculus, Proc. Japan Acad. 42 (1966) 26-29.
  11. C. Jana, M. Pal, A.B. Saeid, (∈, ∈ ∨q)-Bipolar fuzzy BCK/BCI-algebras, Missouri J. Math. Sci. 29 (2017), 139-160.
  12. Y.B. Jun, M.S. Kang, H.S. Kim, Bipolar fuzzy hyper BCK-ideals in hyper BCK-algebras, Iran. J. Fuzzy Syst. 8 (2) (2011), 105-120.
  13. Y.B. Jun, Closed fuzzy ideals in BCI-algebras, Math. Japon. 38 (1) (1993), 199-202.
  14. K. Kawila, C. Udomsetchai, A. Iampan, Bipolar fuzzy UP-algebras, Math. Comput. Appl. 23 (4) (2018), 69.
  15. K.J. Lee, Bipolar fuzzy subalgebras and bipolar fuzzy ideals of BCK/BCI-algebras, Bull. Malays. Math. Sci. Soc. 32 (2009), 361-373.
  16. K.M. Lee, Bipolar-valued fuzzy sets and their operations, Proc. Int. Conf. Intell. Technol. Bangkok, Thailand (2000), 307-312.
  17. K.M. Lee, Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets, J. Fuzzy Log. Intell. Syst. 14 (2004), 125-129.
  18. J. Meng, Y.B. Jun, H. S. Kim, Fuzzy implicative ideals of BCK-algebras, Fuzzy Sets Syst. 89 (1997), 243-248.
  19. J. Meng, Y.B. Jun, BCK-algebras, Kyung Moon Sa Co., Seoul Korea 1994.
  20. G. Muhiuddin, Habib Harizavi, Y.B. Jun, Bipolar-valued fuzzy soft hyper BCK ideals in hyper BCK algebras, Discrete Math. Algorithms Appl. 12 (2) (2020), 2050018.
  21. G. Muhiuddin, Bipolar fuzzy KU-subalgebras/ideals of KU-algebras, Ann. Fuzzy Math. Inform. 8, (3) (2014), 409-418.
  22. G. Muhiuddin, K. P. Shum, New types of (α, β) - fuzzy subalgebras of BCK/BCI-algebras, Int. J. Math. Computer Sci. 14 (2) (2019), 449-464.
  23. G. Muhiuddin, S. Aldhafeeri, Characteristic fuzzy sets and conditional fuzzy subalgebras, J. Comput. Anal. Appl. 25 (8) (2018), 1398-1409.
  24. G. Muhiuddin, A.M. Al-Roqi, Classifications of (alpha, beta)-fuzzy ideals in BCK/BCI-algebras, J. Math. Anal. 7 (6) (2016), 75-82.
  25. G. Muhiuddin, A.M. Al-Roqi, Subalgebras of BCK/BCI-algebras based on (α, β)-type fuzzy sets, J. Comput. Anal. Appl. 18 (6) (2015), 1057-1064.
  26. T. Senapati, K.P. Shum, Cubic subalgebras of BCH-algebras, Ann. Commun. Math. 1 (1) (2018), 65-73.
  27. A.F. Talee, M.Y. Abbasi, A. Basar, On properties of hesitant fuzzy ideals in semigroups, Ann. Commun. Math. 3 (1) (2020), 97-106
  28. S. Thongarsa, P. Burandate, A. Iampan, Some operations of fuzzy sets in UP-algebras with respect to a triangular norm, Ann. Commun. Math. 2 (1) (2019), 1-10
  29. L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353.
  30. W.R. Zhang, Bipolar fuzzy sets, Proc. Fuzzy-IEEE (1998), 835-840.