• Honam Mathematical Journal
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• v.36 no.3
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• pp.623-635
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• 2014

Classications of (${\alpha},{\beta}$)-fuzzy subalgebras of BCK/BCI-algebras are discussed. Relations between (${\in},{\in}{\vee}q$)-fuzzy subalgebras and ($q,{\in}{\vee}q$)-fuzzy subalgebras are established. Given special sets, so called t-q-set and t-${\in}{\vee}q$-set, conditions for the t-q-set and t-${\in}{\vee}q$-set to be subalgebras are considered. The notions of $({\in},q)^{max}$-fuzzy subalgebra, $(q,{\in})^{max}$-fuzzy subalgebra and $(q,{\in}{\vee}q)^{max}$-fuzzy subalgebra are introduced. Conditions for a fuzzy set to be an $({\in},q)^{max}$-fuzzy subalgebra, a $(q,{\in})^{max}$-fuzzy subalgebra and a $(q,{\in}{\vee}q)^{max}$-fuzzy subalgebra are considered.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.3
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• pp.377-379
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• 2003

In this paper, we define a strong fuzzy hyperK-subalgebra and investigate between a strong fuzzy hyperK-subalgebra and a fuzzy hyperK-subalgebra. And then we give some properties of a weak homomorphism and a strong fuzzy hyperK-subalgebra.

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

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.563-576
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• 2021

In this paper, we introduce the notion of intuitionistic fuzzy PMS-subalgebra of a PMS-algebra. The idea of level subsets of an intuitionistic fuzzy PMS-subalgebra of a PMS-algebra is introduced. The relation between intuitionistic fuzzy sets and their level sets in a PMS-algebra is examined, and some interesting results are obtained.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.403-410
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• 2007

Using the belongs to relation (${\in}$) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (${\alpha}$, ${\beta}$)-fuzzy subalgebras where ${\alpha}$ and ${\beta}$ areany two of {${\in}$, q, ${\in}{\vee}q$, ${\in}{\wedge}q$} with ${\alpha}{\neq}{\in}{\wedge}q$ was already introduced, and related properties were investigated (see [3]). In this paper, we give a condition for an (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra to be an (${\in}$, ${\in}$)-fuzzy subalgebra. We provide characterizations of an (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra. We show that a proper (${\in}$, ${\in}$)-fuzzy subalgebra $\mathfrak{A}$ of X with additional conditions can be expressed as the union of two proper non-equivalent (${\in}$, ${\in}$)-fuzzy subalgebras of X. We also prove that if $\mathfrak{A}$ is a proper (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra of a CK/BCI-algebra X such that #($\mathfrak{A}(x){\mid}\mathfrak{A}(x)$ < 0.5} ${\geq}2$, then there exist two prope non-equivalent (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebras of X such that $\mathfrak{A}$ can be expressed as the union of them.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.173-181
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• 2007

Using the belongs to relation ($\in$) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of ($\alpha,\;\beta$)-fuzzy subalgebras where $\alpha,\;\beta$ are any two of $\{{\in},\;q,\;{\in}\;{\vee}\;q,\;{\in}\;{\wedge}\;q\}$ with ${\alpha}\;{\neq}\;{\in}\;{\wedge}\;q$ was introduced, and related properties were investigated in [3]. As a continuation of the paper [3], in this paper, the notion of a fuzzy subalgebra with thresholds is introduced, and its characterizations are obtained. Relations between a fuzzy subalgebra with thresholds and an (${\in},\;{\in}\;{\vee}\;q$)-fuzzy subalgebra are provided.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.203-215
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• 2006

In this note the notion of interval-valued fuzzy BG-algebras (briefly, i-v fuzzy BG-algebras), the level and strong level BG-subalgebra is introduced. Then we state and prove some theorems which determine the relationship between these notions and BG-subalgebras. The images and inverse images of i-v fuzzy BG-subalgebras are defined, and how the homomorphic images and inverse images of i-v fuzzy BG-subalgebra becomes i-v fuzzy BG-algebras are studied.

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

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.385-403
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• 2011

Generalizations of the notion of fuzzy hyper K-subalgebras are considered. The concept of fuzzy hyper K-subalgebras of type (${\alpha},{\beta}$) where ${\alpha}$, ${\beta}$ ${\in}$ {${\in}$, q, ${\in}{\vee}q$, ${\in}{\wedge}q$} and ${\alpha}{\neq}{\in}{\wedge}q$. Relations between each types are investigated, and many related properties are discussed. In particular, the notion of (${\in}$, ${\in}{\vee}q$)-fuzzy hyper K-subalgebras is dealt with, and characterizations of (${\in}$, ${\in}{\vee}q$)-fuzzy hyper K-subalgebras are established. Conditions for an (${\in}$, ${\in}{\vee}q$)-fuzzy hyper K-subalgebra to be an (${\in}$, ${\in}$)-fuzzy hyper K-subalgebra are provided. An (${\in}$, ${\in}{\vee}q$)-fuzzy hyper K-subalgebra by using a collection of hyper K-subalgebras is established. Finally the implication-based fuzzy hyper K-subalgebras are discussed.

• 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.