• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.431-439
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• 2012

Characterizations of $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) are provided. The notion of $\mathcal{N}$-subalgebras of type ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) is introduced, and its characterizations are discussed. Conditions for an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) (resp. ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) to be an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}$) are considered.

• 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.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.377-389
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• 2018

The notion of a uni-soft commutative ideal with thresholds is introduced, and related properties are investigated. Relations between a uni-soft ideal with thresholds and a uni-soft commutative ideal with thresholds are discussed. Conditions for a uni-soft ideal with thresholds to be a uni-soft commutative ideal with the same thresholds are provided. Characterizations of a uni-soft commutative ideal with thresholds are established.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.581-593
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• 2019

The notions of (${\in}$, ${\in}{\vee}q$)-permeable S-value and (${\in}$, ${\in}{\vee}q$)-permeable I-value are introduced, and related properties are investigated. Relations among (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra, (${\in}$, ${\in}{\vee}q$)-fuzzy ideal, (strong) lower and (strong) upper level sets, (${\in}$, ${\in}{\vee}q$)-permeable S-value, (${\in}$, ${\in}{\vee}q$)-permeable I-value, S-energetic set, I-energetic set, right stable set and right vanished set are discussed.