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Issue:(∈, ∈∨q)-Intuitionistic fuzzy ideals of BCK/BCI-algebras: Difference between revisions

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| issue          = [[Notes on Intuitionistic Fuzzy Sets/21/1|"Notes on IFS", Volume 21, 2015, Number 1]], pages 24—42
| issue          = [[Notes on Intuitionistic Fuzzy Sets/21/1|"Notes on IFS", Volume 21, 2015, Number 1]], pages 24—42
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# Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy sets and Systems. 20(1), 87–96.
# Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy sets and Systems. 20(1), 87–96.
# Basnet, D. K., & Singh, L. B. (2011) (∈, ∈∨q)-fuzzy ideal of BG-algebra. International Journal of Algebra, 5(15), 703–708.
# Basnet, D. K., & Singh, L. B. (2011) (∈, ∈∨q)-fuzzy ideal of BG-algebra. International Journal of Algebra, 5(15), 703–708.
# Basnet, D. K. (2010) (α, β)-cut of Intuitionistic Fuzzy Ideals, Notes on Intuitionistic Fuzzy Sets, 16(3), 22–27.
# Basnet, D. K. (2010) [[Issue:(α,β)-cut of intuitionistic fuzzy ideals|(α,β)-cut of Intuitionistic Fuzzy Ideals]], Notes on Intuitionistic Fuzzy Sets, 16(3), 22–27.
# Bhakat, S. K., & Das, P. (1996) (∈, ∈∨q)-fuzzy subgroup. Fuzzy sets and systems, 80, 359–368.
# Bhakat, S. K., & Das, P. (1996) (∈, ∈∨q)-fuzzy subgroup. Fuzzy sets and systems, 80, 359–368.
# Bhakat, S. K., & Das, P. (1999) (∈∨q)-level subset, Fuzzy sets and systems, 103(3), 529–533.
# Bhakat, S. K., & Das, P. (1999) (∈∨q)-level subset, Fuzzy sets and systems, 103(3), 529–533.

Latest revision as of 07:56, 31 May 2016

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http://ifigenia.org/wiki/issue:nifs/21/1/24-42
Title of paper: (∈, ∈∨q)-Intuitionistic fuzzy ideals in BCK/BCI-algebras
Author(s):
S. R. Barbhuiya
Department of Mathematics, Srikishan Sarda College, Hailakandi, 788151, Assam, India
saidurbarbhuiya@gmail.com
Published in: "Notes on IFS", Volume 21, 2015, Number 1, pages 24—42
Download:  PDF (278  Kb, Info)
Abstract: In this paper, we introduced the concept of (∈, ∈∨q)-Intuitionistic fuzzy ideals of BCK-algebras. Characterizations of (∈, ∈∨q)-Intuitionistic fuzzy ideals are given and condition for (∈, ∈∨q)-Intuitionistic fuzzy ideals to be an (∈, ∈)-Intuitionistic fuzzy ideals are established. Cartesian product and intersection of two (∈, ∈∨q)-Intuitionistic fuzzy ideals are also discussed. Homomorphic image and pre-image of (∈, ∈∨q)-Intuitionistic fuzzy ideals are investigated.
Keywords: BCK-algebra, Fuzzy ideal, (∈, ∈∨q)-fuzzy ideal, (∈, ∈∨q)-intuitionistic fuzzy ideal, Homomorphism.
AMS Classification: 06F35, 03G25, 03E72.
References:
  1. Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy sets and Systems. 20(1), 87–96.
  2. Basnet, D. K., & Singh, L. B. (2011) (∈, ∈∨q)-fuzzy ideal of BG-algebra. International Journal of Algebra, 5(15), 703–708.
  3. Basnet, D. K. (2010) (α,β)-cut of Intuitionistic Fuzzy Ideals, Notes on Intuitionistic Fuzzy Sets, 16(3), 22–27.
  4. Bhakat, S. K., & Das, P. (1996) (∈, ∈∨q)-fuzzy subgroup. Fuzzy sets and systems, 80, 359–368.
  5. Bhakat, S. K., & Das, P. (1999) (∈∨q)-level subset, Fuzzy sets and systems, 103(3), 529–533.
  6. Imai, Y. & Iseki, K. (1966) On axiom systems of propositional calculi XIV. Proc. Japan Academy, 42, 19–22.
  7. Kim, C. B. & Kim, H. S. (2008) On BG-algebras. Demonstratio Mathematica, 41, 497–505.
  8. Neggers, J., Kim, H. S. (2002) On B-algebras. Math. Vesnik, 54, 21–29.
  9. Senapati, T., Bhowmik, M., & Pal, M. (2012) Intuitionistic fuzzifications of ideals in BG-algebras. Mathematical Aeterna. 2(9), 761–778.
  10. Yun, Y. B. (2004) On (α, β)-Fuzzy ideals of BCK/BCI–algebras. Scientiae Mathematicae Japonicae Online e-2004, 101–105.
  11. Yun, Y. B., & Kim, K. H. (2000) Intuitionistic fuzzy ideals of of BCK–algebras. Int. J. Math & Math Sci. 24(12), 839–819.
  12. Zadeh, L. A. (1965) Fuzzy sets. Information and Control. 8, 338–353.
  13. Zarandi, A., & Saeid A. B. (2005) On intuitionistic fuzzy ideals of BG-algebras. World Academy of Sciences Engineering and Technology, 5, 187–189.
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