Korean J. Math. Vol. 33 No. 3 (2025) pp.219-229
DOI: https://doi.org/10.11568/kjm.2025.33.3.219

Generalized Lukasiewicz fuzzy subalgebras of BCI-algebras and BCK-algebras

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Published: Sep 30, 2025
Keywords:
$(\alpha, \epsilon)$-Lukasiewicz fuzzy subalgebra, Lukasiewicz $\in$-set, Lukasiewicz $q$-set, Lukasiewicz $O$-set
Mathematics Subject Classification:
03G25, 06F35, 08A72

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Sun Shin Ahn
Department of Mathematics Education, Dongguk University, Seoul 04620, Korea
Young Joo Seo
Research Institute for Natural Sciences, Department of Mathematics, Hanyang University, Seoul 04763, Korea
Young Bae Jun
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea

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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