Fuzzy Set Theoretic Approach to Generalized Ideals in BCK/BCI-Algebras
This paper deals with the study of generalizations of fuzzy subalgebras and fuzzy ideals in BCK/BCI-algebras. In fact, the notions of ∈,∈∨κ~∗,qκ~-fuzzy subalgebras, ∈,∈∨κ~∗,qκ~-fuzzy ideals, and ∈∨κ~∗,qκ~,∈∨κ~∗,qκ~-fuzzy ideals in BCK/BCI-algebras are introduced. Some examples are provided to demons...
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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/5462248 |
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| author | G. Muhiuddin N. Alam S. Obeidat N. M. Khan H. N. Zaidi S. A. K. Kirmani A. Altaleb J. M. Aqib |
| author_facet | G. Muhiuddin N. Alam S. Obeidat N. M. Khan H. N. Zaidi S. A. K. Kirmani A. Altaleb J. M. Aqib |
| author_sort | G. Muhiuddin |
| collection | DOAJ |
| description | This paper deals with the study of generalizations of fuzzy subalgebras and fuzzy ideals in BCK/BCI-algebras. In fact, the notions of ∈,∈∨κ~∗,qκ~-fuzzy subalgebras, ∈,∈∨κ~∗,qκ~-fuzzy ideals, and ∈∨κ~∗,qκ~,∈∨κ~∗,qκ~-fuzzy ideals in BCK/BCI-algebras are introduced. Some examples are provided to demonstrate the logic of the concepts used in this paper. Moreover, some characterizations of these notions are discussed. In addition, the concept of ∈,∈∨κ~∗,qκ~-fuzzy commutative ideals is introduced, and several significant characteristics are discussed. It is shown that for a BCK-algebra A, every ∈,∈∨κ~∗,qκ~-commutative ideal of a BCK-algebra is an ∈,∈∨κ~∗,qκ~-fuzzy ideal, but the converse does not hold in general; a counter example is constructed. |
| format | Article |
| id | doaj-art-277f0ba998d045b9aa0b1e3c833c7aac |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-277f0ba998d045b9aa0b1e3c833c7aac2025-02-03T07:24:17ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/5462248Fuzzy Set Theoretic Approach to Generalized Ideals in BCK/BCI-AlgebrasG. Muhiuddin0N. Alam1S. Obeidat2N. M. Khan3H. N. Zaidi4S. A. K. Kirmani5A. Altaleb6J. M. Aqib7Department of MathematicsDepartment of Basic SciencesDepartment of Basic SciencesDepartment of MathematicsDepartment of Basic SciencesDepartment of Electrical EngineeringDepartment of Basic SciencesDepartment of Software EngineeringThis paper deals with the study of generalizations of fuzzy subalgebras and fuzzy ideals in BCK/BCI-algebras. In fact, the notions of ∈,∈∨κ~∗,qκ~-fuzzy subalgebras, ∈,∈∨κ~∗,qκ~-fuzzy ideals, and ∈∨κ~∗,qκ~,∈∨κ~∗,qκ~-fuzzy ideals in BCK/BCI-algebras are introduced. Some examples are provided to demonstrate the logic of the concepts used in this paper. Moreover, some characterizations of these notions are discussed. In addition, the concept of ∈,∈∨κ~∗,qκ~-fuzzy commutative ideals is introduced, and several significant characteristics are discussed. It is shown that for a BCK-algebra A, every ∈,∈∨κ~∗,qκ~-commutative ideal of a BCK-algebra is an ∈,∈∨κ~∗,qκ~-fuzzy ideal, but the converse does not hold in general; a counter example is constructed.http://dx.doi.org/10.1155/2022/5462248 |
| spellingShingle | G. Muhiuddin N. Alam S. Obeidat N. M. Khan H. N. Zaidi S. A. K. Kirmani A. Altaleb J. M. Aqib Fuzzy Set Theoretic Approach to Generalized Ideals in BCK/BCI-Algebras Journal of Function Spaces |
| title | Fuzzy Set Theoretic Approach to Generalized Ideals in BCK/BCI-Algebras |
| title_full | Fuzzy Set Theoretic Approach to Generalized Ideals in BCK/BCI-Algebras |
| title_fullStr | Fuzzy Set Theoretic Approach to Generalized Ideals in BCK/BCI-Algebras |
| title_full_unstemmed | Fuzzy Set Theoretic Approach to Generalized Ideals in BCK/BCI-Algebras |
| title_short | Fuzzy Set Theoretic Approach to Generalized Ideals in BCK/BCI-Algebras |
| title_sort | fuzzy set theoretic approach to generalized ideals in bck bci algebras |
| url | http://dx.doi.org/10.1155/2022/5462248 |
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