Linear Diophantine Fuzzy Set Theory Applied to <i>BCK/BCI</i>-Algebras
In this paper, we apply the concept of linear Diophantine fuzzy sets in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mi>C</mi><mi>K</mi><mo>/</mo&...
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MDPI AG
2022-06-01
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| author | Ghulam Muhiuddin Madeline Al-Tahan Ahsan Mahboob Sarka Hoskova-Mayerova Saba Al-Kaseasbeh |
| author_facet | Ghulam Muhiuddin Madeline Al-Tahan Ahsan Mahboob Sarka Hoskova-Mayerova Saba Al-Kaseasbeh |
| author_sort | Ghulam Muhiuddin |
| collection | DOAJ |
| description | In this paper, we apply the concept of linear Diophantine fuzzy sets in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mi>C</mi><mi>K</mi><mo>/</mo><mi>B</mi><mi>C</mi><mi>I</mi></mrow></semantics></math></inline-formula>-algebras. In this respect, the notions of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are introduced and some vital properties are discussed. Additionally, characterizations of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are considered. Moreover, the associated results for linear Diophantine fuzzy subalgebras, linear Diophantine fuzzy ideals and linear Diophantine fuzzy commutative ideals are obtained. |
| first_indexed | 2024-03-09T23:08:07Z |
| format | Article |
| id | doaj.art-a8322bd1659c43f7a0a8dac7f2720c96 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:08:07Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-a8322bd1659c43f7a0a8dac7f2720c962023-11-23T17:50:19ZengMDPI AGMathematics2227-73902022-06-011012213810.3390/math10122138Linear Diophantine Fuzzy Set Theory Applied to <i>BCK/BCI</i>-AlgebrasGhulam Muhiuddin0Madeline Al-Tahan1Ahsan Mahboob2Sarka Hoskova-Mayerova3Saba Al-Kaseasbeh4Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaDepartment of Mathematics and Statistics, Abu Dhabi University, Abu Dhabi P.O. Box 15551, United Arab EmiratesDepartment of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle 517325, IndiaDepartment of Mathematics and Physics, University of Defence in Brno, Kounicova 65, 662 10 Brno, Czech RepublicDepartment of Mathematics, Tafila Technical University, Tafila 66110, JordanIn this paper, we apply the concept of linear Diophantine fuzzy sets in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mi>C</mi><mi>K</mi><mo>/</mo><mi>B</mi><mi>C</mi><mi>I</mi></mrow></semantics></math></inline-formula>-algebras. In this respect, the notions of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are introduced and some vital properties are discussed. Additionally, characterizations of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are considered. Moreover, the associated results for linear Diophantine fuzzy subalgebras, linear Diophantine fuzzy ideals and linear Diophantine fuzzy commutative ideals are obtained.https://www.mdpi.com/2227-7390/10/12/2138<i>BCI</i>-algebra<i>BCK</i>-algebralinear Diophantine fuzzy set (<i>LDFS</i>)<i>LDF</i>-subalgebra<i>LDF</i>-ideal<i>LDF</i>-commutative ideal |
| spellingShingle | Ghulam Muhiuddin Madeline Al-Tahan Ahsan Mahboob Sarka Hoskova-Mayerova Saba Al-Kaseasbeh Linear Diophantine Fuzzy Set Theory Applied to <i>BCK/BCI</i>-Algebras Mathematics <i>BCI</i>-algebra <i>BCK</i>-algebra linear Diophantine fuzzy set (<i>LDFS</i>) <i>LDF</i>-subalgebra <i>LDF</i>-ideal <i>LDF</i>-commutative ideal |
| title | Linear Diophantine Fuzzy Set Theory Applied to <i>BCK/BCI</i>-Algebras |
| title_full | Linear Diophantine Fuzzy Set Theory Applied to <i>BCK/BCI</i>-Algebras |
| title_fullStr | Linear Diophantine Fuzzy Set Theory Applied to <i>BCK/BCI</i>-Algebras |
| title_full_unstemmed | Linear Diophantine Fuzzy Set Theory Applied to <i>BCK/BCI</i>-Algebras |
| title_short | Linear Diophantine Fuzzy Set Theory Applied to <i>BCK/BCI</i>-Algebras |
| title_sort | linear diophantine fuzzy set theory applied to i bck bci i algebras |
| topic | <i>BCI</i>-algebra <i>BCK</i>-algebra linear Diophantine fuzzy set (<i>LDFS</i>) <i>LDF</i>-subalgebra <i>LDF</i>-ideal <i>LDF</i>-commutative ideal |
| url | https://www.mdpi.com/2227-7390/10/12/2138 |
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