Linear Diophantine Fuzzy Subspaces of a Vector Space
The notion of a linear diophantine fuzzy set as a generalization of a fuzzy set is a mathematical approach that deals with vagueness in decision-making problems. The use of reference parameters associated with validity and non-validity functions in linear diophantine fuzzy sets makes it more applica...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/3/503 |
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| author | Madeleine Al-Tahan Sarka Hoskova-Mayerova Saba Al-Kaseasbeh Suha Ali Tahhan |
| author_facet | Madeleine Al-Tahan Sarka Hoskova-Mayerova Saba Al-Kaseasbeh Suha Ali Tahhan |
| author_sort | Madeleine Al-Tahan |
| collection | DOAJ |
| description | The notion of a linear diophantine fuzzy set as a generalization of a fuzzy set is a mathematical approach that deals with vagueness in decision-making problems. The use of reference parameters associated with validity and non-validity functions in linear diophantine fuzzy sets makes it more applicable to model vagueness in many real-life problems. On the other hand, subspaces of vector spaces are of great importance in many fields of science. The aim of this paper is to combine the two notions. In this regard, we consider the linear diophantine fuzzification of a vector space by introducing and studying the linear diophantine fuzzy subspaces of a vector space. First, we studied the behaviors of linear diophantine fuzzy subspaces of a vector space under a linear diophantine fuzzy set. Second, and by means of the level sets, we found a relationship between the linear diophantine fuzzy subspaces of a vector space and the subspaces of a vector space. Finally, we discuss the linear diophantine fuzzy subspaces of a quotient vector space. |
| first_indexed | 2024-03-11T09:35:54Z |
| format | Article |
| id | doaj.art-c8c3d373a2074235943c5e826697af2f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:35:54Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c8c3d373a2074235943c5e826697af2f2023-11-16T17:20:32ZengMDPI AGMathematics2227-73902023-01-0111350310.3390/math11030503Linear Diophantine Fuzzy Subspaces of a Vector SpaceMadeleine Al-Tahan0Sarka Hoskova-Mayerova1Saba Al-Kaseasbeh2Suha Ali Tahhan3Department of Mathematics and Statistics, Abu Dhabi University, Abu Dhabi P.O. Box 15551, United Arab EmiratesDepartment of Mathematics and Physics, Faculty of Military Technology, University of Defence, 662 10 Brno, Czech RepublicDepartment of Mathematics, College of Science, Tafila Technical University, P.O. Box 179, Tafila 66110, JordanFaculty of Business, Lebanese International University, Beirut P.O. Box 146404, LebanonThe notion of a linear diophantine fuzzy set as a generalization of a fuzzy set is a mathematical approach that deals with vagueness in decision-making problems. The use of reference parameters associated with validity and non-validity functions in linear diophantine fuzzy sets makes it more applicable to model vagueness in many real-life problems. On the other hand, subspaces of vector spaces are of great importance in many fields of science. The aim of this paper is to combine the two notions. In this regard, we consider the linear diophantine fuzzification of a vector space by introducing and studying the linear diophantine fuzzy subspaces of a vector space. First, we studied the behaviors of linear diophantine fuzzy subspaces of a vector space under a linear diophantine fuzzy set. Second, and by means of the level sets, we found a relationship between the linear diophantine fuzzy subspaces of a vector space and the subspaces of a vector space. Finally, we discuss the linear diophantine fuzzy subspaces of a quotient vector space.https://www.mdpi.com/2227-7390/11/3/503vector spacesubspacelinear diophantine fuzzy set (LDFS)LDF subfieldLDF subspacelevel subspace |
| spellingShingle | Madeleine Al-Tahan Sarka Hoskova-Mayerova Saba Al-Kaseasbeh Suha Ali Tahhan Linear Diophantine Fuzzy Subspaces of a Vector Space Mathematics vector space subspace linear diophantine fuzzy set (LDFS) LDF subfield LDF subspace level subspace |
| title | Linear Diophantine Fuzzy Subspaces of a Vector Space |
| title_full | Linear Diophantine Fuzzy Subspaces of a Vector Space |
| title_fullStr | Linear Diophantine Fuzzy Subspaces of a Vector Space |
| title_full_unstemmed | Linear Diophantine Fuzzy Subspaces of a Vector Space |
| title_short | Linear Diophantine Fuzzy Subspaces of a Vector Space |
| title_sort | linear diophantine fuzzy subspaces of a vector space |
| topic | vector space subspace linear diophantine fuzzy set (LDFS) LDF subfield LDF subspace level subspace |
| url | https://www.mdpi.com/2227-7390/11/3/503 |
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