- Volume 34 Issue 2
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
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.
- 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.
- Z. M. Chen and H. X. Wang, On ideals in BCI-algebras. Math. Japon. 36(3) (1991), 497-501.
- K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Jpn. 23 (1978), 1-26.
- J. Meng and Y. B. Jun, BCK-algebras, Kyungmoon Sa Co. Seoul 1994.
- 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
- 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
- P. Z. Wang, Fuzzy Sets and Falling Shadows of Random Sets, Beijing Normal Univ. Press, People's Republic of China 1985. [In Chinese]
- 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.
- 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
- FALLING FUZZY BCI-COMMUTATIVE IDEALS vol.36, pp.3, 2014, https://doi.org/10.5831/HMJ.2014.36.3.555
- Intuitionistic Falling Shadow Theory with Applications in BCK/BCI-Algebras vol.6, pp.8, 2018, https://doi.org/10.3390/math6080138
- Positive Implicative Ideals of BCK-Algebras Based on Intuitionistic Falling Shadows vol.6, pp.9, 2018, https://doi.org/10.3390/math6090149