GENERALIZED LUKASIEWICZ FUZZY SUBALGEBRAS OF BCI-ALGEBRAS AND BCK-ALGEBRAS

Sun Shin Ahn; Young Joo Seo; Young Bae Jun

doi:10.11568/kjm.2025.33.3.219

GENERALIZED LUKASIEWICZ FUZZY SUBALGEBRAS OF BCI-ALGEBRAS AND BCK-ALGEBRAS

Sun Shin Ahn
, Young Joo Seo
, Young Bae Jun

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

Abstract

The aim of this paper is to generalize ̷Lukasiewicz fuzzy subalgebras in BCK/BCI-algebras. First, the concept of (α, ε)-̷Lukasiewicz fuzzy subalgebras using fuzzy points is defined and examples to explain it are given, and then several properties are investigated. The relationship between ̷Lukasiewicz fuzzy subalgebras and (α, ε)-̷Lukasiewicz fuzzy subalgebras is discussed, and the conditions under which the ε-̷Lukasiewicz fuzzy set to be an (α, ε)-̷Lukasiewicz fuzzy subalgebra are explored. The characterizations of (α, ε)-̷Lukasiewicz fuzzy subalgebras are examined. Conditions under which ̷Lukasiewicz ∈-set, ̷Lukasiewicz q-set and ̷Lukasiewicz O-set can be subalgebras are handled.

Original language	English
Pages (from-to)	219-229
Number of pages	11
Journal	Korean Journal of Mathematics
Volume	33
Issue number	3
DOIs	https://doi.org/10.11568/kjm.2025.33.3.219
State	Published - 30 Sep 2025

Keywords

(Lukasiewicz O-set
(Lukasiewicz qset
(Lukasiewicz ∈-set
(α, ε)- Lukasiewicz fuzzy subalgebra

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10.11568/kjm.2025.33.3.219

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title = "GENERALIZED LUKASIEWICZ FUZZY SUBALGEBRAS OF BCI-ALGEBRAS AND BCK-ALGEBRAS",

abstract = "The aim of this paper is to generalize ̷Lukasiewicz fuzzy subalgebras in BCK/BCI-algebras. First, the concept of (α, ε)-̷Lukasiewicz fuzzy subalgebras using fuzzy points is defined and examples to explain it are given, and then several properties are investigated. The relationship between ̷Lukasiewicz fuzzy subalgebras and (α, ε)-̷Lukasiewicz fuzzy subalgebras is discussed, and the conditions under which the ε-̷Lukasiewicz fuzzy set to be an (α, ε)-̷Lukasiewicz fuzzy subalgebra are explored. The characterizations of (α, ε)-̷Lukasiewicz fuzzy subalgebras are examined. Conditions under which ̷Lukasiewicz ∈-set, ̷Lukasiewicz q-set and ̷Lukasiewicz O-set can be subalgebras are handled.",

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author = "Ahn, \{Sun Shin\} and Seo, \{Young Joo\} and Jun, \{Young Bae\}",

note = "Publisher Copyright: {\textcopyright} The Kangwon-Kyungki Mathematical Society, 2024.",

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doi = "10.11568/kjm.2025.33.3.219",

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AU - Ahn, Sun Shin

AU - Seo, Young Joo

AU - Jun, Young Bae

N1 - Publisher Copyright: © The Kangwon-Kyungki Mathematical Society, 2024.

PY - 2025/9/30

Y1 - 2025/9/30

N2 - The aim of this paper is to generalize ̷Lukasiewicz fuzzy subalgebras in BCK/BCI-algebras. First, the concept of (α, ε)-̷Lukasiewicz fuzzy subalgebras using fuzzy points is defined and examples to explain it are given, and then several properties are investigated. The relationship between ̷Lukasiewicz fuzzy subalgebras and (α, ε)-̷Lukasiewicz fuzzy subalgebras is discussed, and the conditions under which the ε-̷Lukasiewicz fuzzy set to be an (α, ε)-̷Lukasiewicz fuzzy subalgebra are explored. The characterizations of (α, ε)-̷Lukasiewicz fuzzy subalgebras are examined. Conditions under which ̷Lukasiewicz ∈-set, ̷Lukasiewicz q-set and ̷Lukasiewicz O-set can be subalgebras are handled.

AB - The aim of this paper is to generalize ̷Lukasiewicz fuzzy subalgebras in BCK/BCI-algebras. First, the concept of (α, ε)-̷Lukasiewicz fuzzy subalgebras using fuzzy points is defined and examples to explain it are given, and then several properties are investigated. The relationship between ̷Lukasiewicz fuzzy subalgebras and (α, ε)-̷Lukasiewicz fuzzy subalgebras is discussed, and the conditions under which the ε-̷Lukasiewicz fuzzy set to be an (α, ε)-̷Lukasiewicz fuzzy subalgebra are explored. The characterizations of (α, ε)-̷Lukasiewicz fuzzy subalgebras are examined. Conditions under which ̷Lukasiewicz ∈-set, ̷Lukasiewicz q-set and ̷Lukasiewicz O-set can be subalgebras are handled.

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KW - (Lukasiewicz qset

KW - (Lukasiewicz ∈-set

KW - (α, ε)- Lukasiewicz fuzzy subalgebra

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JO - Korean Journal of Mathematics

JF - Korean Journal of Mathematics

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ER -

GENERALIZED LUKASIEWICZ FUZZY SUBALGEBRAS OF BCI-ALGEBRAS AND BCK-ALGEBRAS

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Keywords

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