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

Authors

  • Eun Hwan Roh Department of Mathematics Education, Chinju National University of Education
  • Eunsuk Yang Department of Philosophy, Jeonbuk National University, Jeonju 54896, Korea
  • Young Bae Jun Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i4.4933

Keywords:

intuitionistic fuzzy point, intuitionistic fuzzy (ordered) subalgebra,, $q_{(t,s)}$-level set

Abstract

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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Published

2023-10-30

Issue

Vol. 16 No. 4: (October 2023)

Section

Nonlinear Analysis

License

Copyright (c) 2023 European Journal of Pure and Applied Mathematics

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How to Cite

Ideals of BCK-algebras and BCI-algebras Based on a New Form of Fuzzy Set. (2023). European Journal of Pure and Applied Mathematics, 16(4), 2009-2024. https://doi.org/10.29020/nybg.ejpam.v16i4.4933