基于模糊集新形式的bck -代数和bci -代数理想

IF 1 Q1 MATHEMATICS European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI:10.29020/nybg.ejpam.v16i4.4933

Eun Hwan Roh, Eunsuk Yang, Young Bae Jun

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引用次数: 0

摘要

研究了基于$Y_J^{\varepsilon}$-模糊集的BCK/BCI代数的理想。首先研究了$Y_J^{\varepsilon}$-模糊集的水平集的基本性质。引入了BCK/ bci代数中的(闭)$Y_J^{\varepsilon}$-模糊理想的概念，并研究了其若干性质。讨论了$Y_J^{\varepsilon}$-模糊理想与$Y_J^{\varepsilon}$-模糊子代数之间的关系，并辨识了$Y_J^{\varepsilon}$-模糊理想与模糊理想之间的关系。利用y水平集建立了(闭)$Y_J^{\varepsilon}$-模糊理想的表征。探讨了$Y_J^{\varepsilon}$-fuzzy理想闭合的充分必要条件，并给出了$Y_J^{\varepsilon}$-fuzzy子代数为$Y_J^{\varepsilon}$-fuzzy理想的条件。

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Ideals of BCK-algebras and BCI-algebras Based on a New Form of Fuzzy Set

Ideals in BCK/BCI algebra based on $Y_J^{\varepsilon}$-fuzzy sets are studied. The fundamental properties of the level set of $Y_J^{\varepsilon}$-fuzzy sets are investigate first. The concept of (closed) $Y_J^{\varepsilon}$-fuzzy ideals in BCK/BCI-algebras is introduces, and several properties are investigated. The relationship between $Y_J^{\varepsilon}$-fuzzy ideal and $Y_J^{\varepsilon}$-fuzzy subalgebra are discussed, and also the relationship between $Y_J^{\varepsilon}$-fuzzy ideal and fuzzy ideal is identified. The characterization of (closed) $Y_J^{\varepsilon}$-fuzzy ideal using the Y-level set is established. The necessary and sufficient conditions for $Y_J^{\varepsilon}$-fuzzy ideal to be closed is explored, and conditions for $Y_J^{\varepsilon}$-fuzzy subalgebra to be $Y_J^{\varepsilon}$-fuzzy ideal are provided.

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