• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.2
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• pp.243-246
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• 2003

In this paper we define a weak positive implicative hyperBCK-ideal of hyperBCK-algebra. Also we investigate that every positive implicative hyperBCK-algebra is a positive implicative hyperK-algebra and then we prove that every positive implicative hyperK-algebra is a weak positive implicative hyperk-algebra.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.333-339
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• 2009

In this manuscript, we introduce the concept of an atomic subset of the hyper BCK-algebra and study its properties. Also, we give a characterization of the atomic hyper BCK-algebra and show that there are exactly (up to isomorphism) n atomic hyper BCK-algebras H with |H| = n for any natural number n.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.643-659
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• 2016

In this paper, we investigate some new results in MV-algebras and (strong) hyper MV-algebras. We show that for any infinite countable set M, we can construct an MV-algebra and a strong hyper MV-algebra on M. Specially, for any infinite totally bounded set, we can construct a strong hyper MV-algebra on it. Then by considering the concept of fundamental relation on hyper MV-algebras, we define the notion of fundamental MV-algebra and prove that any MV-algebra is a fundamental MV-algebra. In practical, we show that any infinite countable MV-algebra is a fundamental MV-algebra of itself, but it is not correct for finite MV-algebras.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.123-137
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• 2003

In this note first we define the notions of weak implicative and implicative hyper K-ideals of a hyper K-algebra H. Then we state and prove some theorems which determine the relationship between these notions and (weak) hyper K-ideals. Also we give some relations between these notions and all types of positive implicative hyper K-ideals. Finally we classify the implicative hyper K-ideals of a hyper K-algebra of order 3.

• Honam Mathematical Journal
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• v.28 no.1
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• pp.57-67
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• 2006

we apply the hyperstructures to BCC-algebras, and introduce the concept of a hyper BCC-algebra which is a generalization of a BCC-algebra, and investigates some related properties. We also introduce the notion of a hyper BCC-subalgebra, BCC-scalar element and a hyper BCC-ideal, and discuss related properties.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.131-139
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• 2010

Several types of skeletons in a hyper MV-algebra are introduced, and their relations are investigated.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.43-52
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• 2003

The fuzzification of positive implicative hyper K-ideals in hyper K-algebras is considered, Relations between fuzzy positive implicative hyper K-ideal and fuzzy hyper K-ideal are given. Characterizations of fuzzy positive implicative hyper K-ideals are provided. Using a family of positive implicative hyper K-ideals we make a fuzzy positive implicative hyper K-ideal. Using the notion of a fuzzy positive implicative hyper K-ideal, a weak hyper K-ideal is established.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.141-162
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• 2005

In this paper, by considering the notion of hyperK-algebras of order 3 (which satisfies the simple or normal condition), we state and prove some theorems which determine the relationships between (weak) hyperK-ideals and positive implicative hyperK-ideals of type $1,{\ldots},8$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.303-303
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• 2019

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.679-695
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• 2013

In this paper, the concept of ($\bar{\in},\bar{\in}{\vee}\var{q}$)-fuzzy hyper K-subalgebras and fuzzy hyper K-subalgebras with thresholds are introduced, and related properties and characterizations are discussed.