Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

FALLING SHADOWS APPLIED TO SUBALGEBRAS AND IDEALS OF BCK/BCI-ALGEBRAS

  • Jun, Young-Bae (Department of Mathematics Education (and RINS), Gyeongsang National University) ;
  • Park, Chul-Hwan (School of Digital,Mechanics, Ulsan College)
  • Received : 2011.08.25
  • Accepted : 2012.04.12
  • Published : 2012.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

falling subalgebra/ideal of a BCK/BCI-algebra is introduced. Relations between falling subalgebras and falling ideals are given. Relations between fuzzy subalgebras/ideals and falling sub-algebras/ideals are provided. A characterization of a falling ideal is established.

Keywords

References

  1. Z. M. Chen and H. X. Wang, On ideals in BCI-algebras. Math. Japon. 36(3) (1991), 497-501.
  2. I. R. Goodman, Fuzzy sets as equivalence classes of random sets, in "Recent Developments in Fuzzy Sets and Possibility Theory"(R. Yager, Ed.), Pergamon, New York 1982, pp. 327-343.
  3. K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Jpn. 23 (1978), 1-26.
  4. J. Meng and Y. B. Jun, BCK-algebras, Kyungmoon Sa Co. Seoul 1994.
  5. S. K. Tan, P. Z. Wang and X. Z. Zhang, Fuzzy inference relation based on the theory of falling shadows, Fuzzy Sets and Systems 53 (1993), 179-188. https://doi.org/10.1016/0165-0114(93)90171-D
  6. S. K. Tan, P. Z. Wang and E. S. Lee, Fuzzy set operations based on the theory of falling shadows, J. Math. Anal. Appl. 174 (1993), 242-55. https://doi.org/10.1006/jmaa.1993.1114
  7. P. Z. Wang, Fuzzy Sets and Falling Shadows of Random Sets, Beijing Normal Univ. Press, People's Republic of China 1985. [In Chinese]
  8. P. Z. Wang and E. Sanchez, Treating a fuzzy subset as a projectable random set, in "Fuzzy Information and Decision" (M. M. Gupta and E. Sanchez, Eds.), Pergamon, New York 1982, pp. 212-219.
  9. X. H. Yuan and E. S. Lee, A fuzzy algebraic system based on the theory of falling shadows, J. Math. Anal. Appl. 208 (1997), 243-251. https://doi.org/10.1006/jmaa.1997.5331

Cited by

  1. FALLING FUZZY BCI-COMMUTATIVE IDEALS vol.36, pp.3, 2014, https://doi.org/10.5831/HMJ.2014.36.3.555
  2. Intuitionistic Falling Shadow Theory with Applications in BCK/BCI-Algebras vol.6, pp.8, 2018, https://doi.org/10.3390/math6080138
  3. Positive Implicative Ideals of BCK-Algebras Based on Intuitionistic Falling Shadows vol.6, pp.9, 2018, https://doi.org/10.3390/math6090149