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FALLING FUZZY COMMUTATIVE IDEALS OF BCK-ALGEBRAS

  • Jun, Young-Bae (Department of Mathematics Education, Gyeongsang National University) ;
  • Kang, Min-Su (Department of Mathematics, Hanyang University)
  • Received : 2010.08.25
  • Accepted : 2011.02.20
  • Published : 2011.02.28

Abstract

Based on the theory of falling shadows and fuzzy sets, the notion of a falling fuzzy commutative ideal of a BCK-algebra is introduced. Relations between falling fuzzy commutative ideals and falling fuzzy ideals are investigated.

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. K. Iseki & S. Tanaka: An introduction to the theory of BCK-algebras. Math. Jpn. 23 (1978), 1-26.
  3. Y.B. Jun & C.H. Park: Falling shadows applied to subalgebras and ideals of BCK/BCI-algebras. Chaos, Solitions and Fractals (submitted).
  4. Y.B. Jun & 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
  5. J. Meng & Y.B. Jun: BCK-algebras. Kyungmoon Sa Co. Seoul 1994.
  6. S.K. Tan, P.Z. Wang & 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
  7. S.K. Tan, P.Z. Wang & 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
  8. P.Z. Wang: Fuzzy Sets and Falling Shadows of Random Sets. Beijing Normal Univ. Press, People's Republic of China, 1985. [In Chinese]
  9. P.Z. Wang & 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.

Cited by

  1. CHARACTERIZATIONS OF FALLING FUZZY IDEALS vol.34, pp.1, 2012, https://doi.org/10.5831/HMJ.2012.34.1.125