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International Journal of Mathematics and Mathematical Sciences
Volume 2010, Article ID 819463, 11 pages
Research Article

Implicative Ideals of BCK-Algebras Based on the Fuzzy Sets and the Theory of Falling Shadows

1Department of Mathematics Education and RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea
2Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea
3Department of Mathematics, University of Ulsan, Ulsan 680-749, Republic of Korea

Received 11 March 2010; Revised 14 November 2010; Accepted 20 December 2010

Academic Editor: Heinz Gumm

Copyright © 2010 Young Bae Jun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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