• 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.

• Journal of applied mathematics & informatics
• /
• v.8 no.1
• /
• pp.261-272
• /
• 2001

The intuitionistic fuzzification of a subalgebra in a BCK/BCI-algebra is considered, and related results are investigated. The notion of equivalence relations on the family of all intuitionistic fuzzy subalgebras of a BCK/BCI-algebra is introduced, and then some properties are discussed.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.795-807
• /
• 2009

The concepts of fuzzy pseudo ideals (resp. fuzzy pseudo p-ideals, associative fuzzy pseudo ideals, fuzzy pseudo q-ideals and fuzzy pseudo a-ideals) in a pseudo BCI-algebra are introduced, and related properties are investigated. Conditions for a fuzzy pseudo ideal to be a fuzzy pseudo p-ideal (resp. fuzzy pseudo q-ideal) are provided. A characterization and properties of an associative fuzzy pseudo ideal are given.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.3
• /
• pp.279-286
• /
• 2007

Using t-norm T and s-norm S, we introduce the notion of intuitionistic (T, S)-normed fuzzy subalgebra in BCK/BCI-algebra, and some related properties are investigated.

• Journal of the Chungcheong Mathematical Society
• /
• v.9 no.1
• /
• pp.1-9
• /
• 1996

In this paper, we consider the quotient algebra of BCI-semigroups, and obtain some isomorphism theorems of BCI-semigroups.

• Communications of the Korean Mathematical Society
• /
• v.17 no.3
• /
• pp.403-407
• /
• 2002

In this note We discuss the Uniformity in BCI-algebras using Zhang's congruence relation.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.4
• /
• pp.395-404
• /
• 2020

Based on a sub-BCK-algebra K of a BCI-algebra X, the notions of fuzzy (K, ε)-subalgebras, fuzzy (K, ε)-ideals and fuzzy commutative (K, ε)-ideals are introduced, and their relations/properties are investigated. Conditions for a fuzzy subalgebra/ideal to be a fuzzy (K, ε)-subalgebra/ideal are provided.

• Kyungpook Mathematical Journal
• /
• v.55 no.4
• /
• pp.859-870
• /
• 2015

The notion of quasi-valuation maps based on a subalgebra and an ideal in BCK/BCI-algebras is introduced, and then several properties are investigated. Relations between a quasi-valuation map based on a subalgebra and a quasi-valuation map based on an ideal is established. In a BCI-algebra, a condition for a quasi-valuation map based on an ideal to be a quasi-valuation map based on a subalgebra is provided, and conditions for a real-valued function on a BCK/BCI-algebra to be a quasi-valuation map based on an ideal are discussed. Using the notion of a quasi-valuation map based on an ideal, (pseudo) metric spaces are constructed, and we show that the binary operation * in BCK-algebras is uniformly continuous.

• East Asian mathematical journal
• /
• v.23 no.1
• /
• pp.75-82
• /
• 2007

In this paper we give a concrete computational method to characterize $S_3$-algebras.

• Communications of the Korean Mathematical Society
• /
• v.10 no.2
• /
• pp.269-273
• /
• 1995

In this paper, we introduce the notion of $\lambda$-associative BCI-algebras, investigate important properties of such algebras, and discuss the structure of it.