Missouri Journal of Mathematical Sciences

Int-soft Implicative hyper $BCK$-ideals in hyper $BCK$-algebras

Rajab Ali Borzooei, Xiao Long Xin, Eun Hwan Roh, and Young Bae Jun

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


The notion of an int-soft (weak) implicative hyper BCK-ideal is introduced, and related properties are investigated. Relations between an int-soft weak implicative hyper BCK-ideal, an int-soft implicative hyper BCK-ideal, an int-soft hyper BCK-ideal, and an int-soft strong hyper BCK-ideal are considered, and characterizations of an int-soft weak implicative hyper BCK-ideal are discussed. Conditions for an int-soft hyper BCK-ideal to be an int-soft weak implicative hyper BCK-ideal are provided. Using an int-soft weak implicative hyper BCK-ideal, a new int-soft weak implicative hyper BCK-ideal is established. Finally, we show the hyper homomorphic preimage of an int-soft implicative hyper BCK-ideal is also an int-soft implicative hyper BCK-ideal.

Article information

Missouri J. Math. Sci., Volume 31, Issue 2 (2019), 152-163.

First available in Project Euclid: 16 November 2019

Permanent link to this document

Digital Object Identifier

Primary: 06F35: BCK-algebras, BCI-algebras [See also 03G25]
Secondary: 03G25: Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35] 06D72: Fuzzy lattices (soft algebras) and related topics

int-soft (weak, strong, $s$-weak) hyper BCK-ideal int-soft weak implicative hyper BCK-ideal int-soft implicative hyper BCK-ideal


Borzooei, Rajab Ali; Xin, Xiao Long; Roh, Eun Hwan; Jun, Young Bae. Int-soft Implicative hyper $BCK$-ideals in hyper $BCK$-algebras. Missouri J. Math. Sci. 31 (2019), no. 2, 152--163. doi:10.35834/2019/3102152. https://projecteuclid.org/euclid.mjms/1573873231

Export citation


  • R. A. Borzooei and M. Bakhshi, (Weak) implicative hyper BCK-ideals, Quasigroups Related Systems, 12 (2004), 13–28.
  • D. Chen, E. C. C. Tsang, D. S. Yeung, and X. Wang, The parametrization reduction of soft sets and its applications, Comput. Math. Appl., 49 (2005), 757–763.
  • Y. B. Jun and S. Z. Song, Hyper BCK-ideals based on soft set theory, Asian-European J. Math., 9.3 (2016), 1650065 (12 pages).
  • Y. B. Jun and X. L. Xin, Implicative hyper BCK-ideals of hyper BCK-algebras, Math. Japon., 52.3 (2000), 435–443.
  • Y. B. Jun, X. L. Xin, E. H. Roh, and M. M. Zadehi, Strong hyperBCK-ideals of hyperBCK-algerbas, Math. Japon., 51.3 (2000), 493–498.
  • Y. B. Jun, M. M. Zahedi, X. L. Xin, and R. A. Borzoei, On hyper BCK-algebras, Italian J. Pure Appl. Math., 8 (2000), 127–136.
  • P. K. Maji, R. Biswas, and A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555–562.
  • P. K. Maji, A. R. Roy, and R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002), 1077–1083.
  • F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934), 45–49.
  • D. Molodtsov, Soft set theory - First results, Comput. Math. Appl., 37 (1999), 19–31.
  • A. N. Prior, Formal Logic, 2nd ed., Clarendon Press, Oxford, 1962.