• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.531-542
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• 2011

The notion of bipolar fuzzy a-ideals of BCI-algebras is introduced, and their properties are investigated. Relations between bipolar fuzzy subalgebras, bipolar fuzzy ideals and bipolar fuzzy a-ideals are discussed. Conditions for a bipolar fuzzy ideal to be a bipolar fuzzy a-ideal are provided. Characterizations of bipolar fuzzy a-ideals are given. Using a finite collection of a-ideals, a bipolar fuzzy a-ideal is established.

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

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.339-348
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• 2015

Using the notion of soft sets, the concepts of the soft transfer, support and soft algebraic extension of an int-soft subalgebra and ideal in BCK/BCI-algebras are introduced, and related properties are investigated. Conditions for a soft set to be an int-soft subalgebra and ideal are provided. Regarding the notion of support, conditions for the soft transfer of a soft set to be an int-soft subalgebra and ideal are considered.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1105-1115
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• 2022

The main objective of this paper is to introduce the notion of AMR-algebra and its generalization, and to compare them with other algebras such as BCK, BCI, BCH, · · ·, etc. We show moreover that the K-part of AMR-algebra is an abelian group, and the weak AMR-algebra is also an abelian group and generalizes many known algebras like BCI, BCH, and G.

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

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

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.33-41
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• 1999

In this paper, we introduce a new notion, called an QS-algebra, which is related to the areas of BCI/BCK-algebras and discuss the G-part of QS-algebras.

• Communications of the Korean Mathematical Society
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• v.3 no.2
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• pp.119-124
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• 1988

• East Asian mathematical journal
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• v.9 no.1
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• pp.1-6
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• 1993

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

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1937-1956
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• 2013

The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of union-soft sets is introduced, and its application to BCK/BCI-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are introduced, and related properties and relations are investigated. Conditions for a union-soft ideal to be closed are provided. Conditions for a union-soft ideal to be a union-soft commutative ideal are also provided. Characterizations of (closed) union-soft ideals and union-soft commutative ideals are established. Extension property for a union-soft commutative ideal is established.