Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

CHARACTERIZATIONS OF FALLING FUZZY IDEALS

  • Jun, Young-Bae (Department of Mathematics Education (and RINS), Gyeongsang National University) ;
  • Song, Seok-Zun (Department of Mathematics, Jeju National University) ;
  • Roh, Eun-Hwan (Department of Mathematics Education, Chinju National University of Education)
  • Received : 2012.02.28
  • Accepted : 2012.03.14
  • Published : 2012.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

Relations among falling fuzzy ideals, falling fuzzy implicative ideals, falling fuzzy positive implicative ideals and falling fuzzy commutative ideals are considered. Characterizations of falling fuzzy positive implicative ideals and other related ideals are discussed.

Keywords

References

  1. 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).
  2. Y. B. Jun, S. M. Hong, J. Meng and X. L. Xin, Characterizations of fuzzy positive implicative ideals in BCK-algebras, Math. Japon. 40 (1994) 503-507.
  3. Y. B. Jun and M. S. Kang, Fuzzy positive implicative ideals of BCK-algebras based on the theory of falling shadows, Comput. Math. Appl. 61 (2011) 62-67.
  4. Y. B. Jun and M. S. Kang, Falling fuzzy commutative ideals of BCK-algebras, J. Korean Soc. Math. Edu. Ser. B: Pure Appl. Math. 18 (2011) 41-50. https://doi.org/10.7468/jksmeb.2011.18.1.041
  5. Y. B. Jun, M. S. Kang and C. H. Park, Implicative ideals of BCK-algebras based on the fuzzy sets and the theory of falling shadows, Internat. J. Math. Math. Sci. Volume 2010, Article ID 819463, 11 pages.
  6. Y. B. Jun and C. H. Park, Falling shadows applied to subalgebras and ideals of BCK/BCI-algebras, Chaos, Solitions and Fractals (submitted).
  7. Y. B. Jun, M. A. Ozturk and A. Firat, Characterizations of falling fuzzy positive implicative ideals in BCK-algebras, Appl. Soft Comput. (submitted).
  8. Y. B. Jun and E. H. Roh, Fuzzy commutative ideals of BCK-algebras, Fuzzy Sets and Systems 64 (1994) 401-405. https://doi.org/10.1016/0165-0114(94)90163-5
  9. J. Meng and Y. B. Jun, BCK-algebras, Kyungmoon Sa Co. Seoul 1994.
  10. S. M. Mostafa, Fuzzy implicative ideals of BCK-algebras, Fuzzy Sets and Systems 87 (1997) 361-368. https://doi.org/10.1016/S0165-0114(96)00017-6
  11. 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) 242-255. https://doi.org/10.1006/jmaa.1993.1114
  12. 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
  13. P. Z. Wang, Fuzzy Sets and Falling Shadows of Random Sets, Beijing Normal Univ. Press, People's Republic of China, 1985. [In Chinese]
  14. P. Z. Wang and E. Sanchez, Treating a fuzzy subset as a projectable random set, in: M. M. Gupta, E. Sanchez, Eds., "Fuzzy Information and Decision" (Pergamon, New York, 1982) 212-219.
  15. O. G. Xi, Fuzzy BCK-algebras, Math. Japon. 36 (1991) 935-942.

Cited by

  1. Positive Implicative Ideals of BCK-Algebras Based on Intuitionistic Falling Shadows vol.6, pp.9, 2018, https://doi.org/10.3390/math6090149