• Journal of applied mathematics & informatics
• /
• v.11 no.1_2
• /
• pp.255-263
• /
• 2003

Fuzzifications of n-fold quasi-associative ideals are considered. Conditions for a fuzzy ideal to be a fuzzy n-fold quasi-associative ideal are given. Using a collection of n-fold quasi-associative ideals, fuzzy n-fold quasi-associative ideals are constructed. Finally, the extension property for fuzzy n-fold quasi-associative ideals is established.

• Honam Mathematical Journal
• /
• v.31 no.1
• /
• pp.125-136
• /
• 2009

After the introduction of fuzzy sets by Zadeh, there have been a number of generaizations of this fundamental concept. The notion of bipolar-valued fuzzy sets introduced by Lee is one among them. In this paper, we apply the concept of a bipolar-valued fuzzy set to quasi-associative ideals in BCI-algebras. The notion of a bipolar fuzzy quasi-associative ideal of a BCI-algebra is introduced, and some related properties are investigated. Characterizations of a bipolar fuzzy quasi-associative ideal are given. Extension property for a bipolar fuzzy QA-ideal is established.

• Honam Mathematical Journal
• /
• v.44 no.2
• /
• pp.148-164
• /
• 2022

The main purpose of this paper is to apply the notion of hesitant fuzzy sets to an algebraic structure, so called a BCI-algebra. The primary goal of the study is to define hesitant fuzzy p-ideals and hesitant fuzzy quasi-associative ideals in BCI-algebras, and to investigate their properties and relations.

• Journal of applied mathematics & informatics
• /
• v.10 no.1_2
• /
• pp.51-62
• /
• 2002

The present paper gives a new construction of a quotient BCI(BCK)-algebra X/${\mu}$ by a fuzzy ideal ${\mu}$ in X and establishes the Fuzzy Homomorphism Fundamental Theorem. We show that if ${\mu}$ is a fuzzy ideal (closed fuzzy ideal) of X, then X/${\mu}$ is a commutative (resp. positive implicative, implicative) BCK(BCI)-algebra if and only if It is a fuzzy commutative (resp. positive implicative, implicative) ideal of X Moreover we prove that a fuzzy ideal of a BCI-algebra is closed if and only if it is a fuzzy subalgebra of X We show that if the period of every element in a BCI-algebra X is finite, then any fuzzy ideal of X is closed. Especiatly, in a well (resp. finite, associative, quasi-associative, simple) BCI-algebra, any fuzzy ideal must be closed.