• Honam Mathematical Journal
• /
• v.36 no.3
• /
• pp.555-568
• /
• 2014

On the basis of the theory of a falling shadow and fuzzy sets, the notion of a falling fuzzy BCI-commutative ideal of a BCI-algebra is introduced. Relations between falling fuzzy BCI-commutative ideals and falling fuzzy ideals are given. Relations between fuzzy BCI-commutative ideals and falling fuzzy BCI-commutative ideals are provided. Characterizations of a falling fuzzy BCI-commutative ideal are established, and conditions for a falling fuzzy (closed) ideal to be a falling fuzzy BCI-commutative ideal are considered.

• The Pure and Applied Mathematics
• /
• v.19 no.3
• /
• pp.251-262
• /
• 2012

Based on the theory of a falling shadow which was first formulated by Wang([14]), a theoretical approach of the ideal structure in BH-algebras is established. The notions of a falling subalgebra, a falling ideal, a falling strong ideal, a falling $n$-fold strong ideal and a falling translation ideal of a BH-algebra are introduced. Some fundamental properties are investigated. Relations among a falling subalgebra, a falling ideal and a falling strong ideal, a falling $n$-fold strong ideal are stated. A relation between a fuzzy subalgebra/ideal and a falling subalgebra/ideal is provided.

• The Pure and Applied Mathematics
• /
• v.18 no.1
• /
• pp.41-50
• /
• 2011

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.

• Honam Mathematical Journal
• /
• v.34 no.1
• /
• pp.125-133
• /
• 2012

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.

• Honam Mathematical Journal
• /
• v.34 no.2
• /
• pp.135-144
• /
• 2012

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.