• 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.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.263-271
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• 2012

Any BCK-ideal of a BCC-algebra can be decomposed into the union of some sets. The notion of a complicatedness and a derivation for a BCC-algebra is introduced and some related properties are obtained.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.489-495
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• 2009

Any BCK-ideal of a d-algebra can be decomposed into the union of some sets. The notion of a complicated d-algebra is introduced and some related properties are obtained.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.601-611
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• 1996

In this paper, we introduce the notion of weakly associative BCI-algebras and investigate structure of it. Some of characterizations of elements of the quasi-associative part Q(X) of a BCI-algebra X are shown.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.507-514
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• 2018

Let $\{{\varphi}_n\}_{n{\geq}1}$ be a sequence of analytic self-maps of ${\mathbb{D}}$. It is proved that if the union set of the ranges of the composition operators $C_{{\varphi}_n}$ on the weighted Bergman spaces contains the disk algebra, then ${\varphi}_k$ is an automorphism of ${\mathbb{D}}$ for some $k{\geq}1$.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.445-453
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• 2007

The notion of strong deductive system of a BL-algebra is introduced, and a characterization of a strong deductive system is given. A relation between a strong deductive system and a deductive system is given. It will be seen that every strong deductive system can be expressed as the union of special sets.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.65-77
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• 2020

In this paper, for any non-empty subsets A, I of a pseudo BCI-algebra X, we introduce the concept of pseudo p-closure of A with respect to I, denoted by A^pc_I, and investigate some related properties. Applying this concept, we state a necessary and sufficient condition for a pseudo BCI-algebra 1) to be a p-semisimple pseudo BCI-algebra; 2) to be a pseudo BCK-algebra. Moreover, we show that A^pc_{0} is the least positive pseudo ideal of X containing A, and characterize it by the union of some branches. We also show that the set of all pseudo ideals of X which A^pc_I = A, is a complete lattice. Finally, we prove that this notion can be used to define a closure operation.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.89-104
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• 2020

In this paper, we connect (α, β) union soft sets and their ideal related properties with KU-algebras. In particular, we will study (α, β)-union soft sets, (α, β)-union soft ideals, (α, β)-union soft commutative ideals and ideal relations in KU-algebras. Finally, a characterization of ideals in KU-algebras in terms of (α, β)-union soft sets have been provided.

• Honam Mathematical Journal
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• v.37 no.2
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• pp.207-219
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• 2015

As a generalization of BH-algebras, the notion of pseudo BH-algebra is introduced, and some of their properties are investigated. The notions of pseudo ideals, pseudo atoms, pseudo strong ideals, and pseudo homomorphisms in pseudo BH-algebras are introduced. Characterizations of their properties are provided. We show that every pseudo homomorphic image and preimage of a pseudo ideal is also a pseudo ideal. Any pseudo ideal of a pseudo BH-algebra can be decomposed into the union of some sets. The notion of pseudo complicated BH-algebra is introduced and some related properties are obtained.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.457-463
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• 2007

We show that any filter of Tarski algebra can be de-composed into the union of some sets. Moreover, we introduce the notion of expansions of filters in Tarski algebras, and discuss the notion of ${\sigma}$-primary filters in Tarski algebras. Finally, we show that there is no non-trivial quadratic Tarski algebras on a field X with $|X|{\geq}3$.