Level Operators over Intuitionistic Fuzzy Index Matrices
The index matrix (IM) is an extension of the ordinary matrix with indexed rows and columns. Over IMs’ standard matrix operations are defined and a lot of other ones that do not exist in the standard case. Intuitionistic fuzzy IMs (IFIMs) are modification of the IMs, when their elements are intuition...
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| Format: | Article |
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MDPI AG
2021-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/4/366 |
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| author | Krassimir Atanassov Peter Vassilev Olympia Roeva |
| author_facet | Krassimir Atanassov Peter Vassilev Olympia Roeva |
| author_sort | Krassimir Atanassov |
| collection | DOAJ |
| description | The index matrix (IM) is an extension of the ordinary matrix with indexed rows and columns. Over IMs’ standard matrix operations are defined and a lot of other ones that do not exist in the standard case. Intuitionistic fuzzy IMs (IFIMs) are modification of the IMs, when their elements are intuitionistic fuzzy pairs (IFPs). Extended IFIMs are IFIMs whose indices of the rows and columns are evaluated by IFPs. Different operations, relations and operators over IFIMs, and some specific ones, are defined for EIFIMs. In the paper, twelve new level operators are defined for EIFIMs and in the partial case, over IFIMs. The proposed level operators fall into two groups: operators that change the values of the EIFIM elements and operators that change the IFPs associated to the indices of the rows and columns. The basic properties of the operators are studied. |
| first_indexed | 2024-03-09T00:57:48Z |
| format | Article |
| id | doaj.art-90bfbfc577544caa900c2a1e0f0eebe7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T00:57:48Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-90bfbfc577544caa900c2a1e0f0eebe72023-12-11T16:46:23ZengMDPI AGMathematics2227-73902021-02-019436610.3390/math9040366Level Operators over Intuitionistic Fuzzy Index MatricesKrassimir Atanassov0Peter Vassilev1Olympia Roeva2Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, 1113 Sofia, BulgariaDepartment of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, 1113 Sofia, BulgariaDepartment of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, 1113 Sofia, BulgariaThe index matrix (IM) is an extension of the ordinary matrix with indexed rows and columns. Over IMs’ standard matrix operations are defined and a lot of other ones that do not exist in the standard case. Intuitionistic fuzzy IMs (IFIMs) are modification of the IMs, when their elements are intuitionistic fuzzy pairs (IFPs). Extended IFIMs are IFIMs whose indices of the rows and columns are evaluated by IFPs. Different operations, relations and operators over IFIMs, and some specific ones, are defined for EIFIMs. In the paper, twelve new level operators are defined for EIFIMs and in the partial case, over IFIMs. The proposed level operators fall into two groups: operators that change the values of the EIFIM elements and operators that change the IFPs associated to the indices of the rows and columns. The basic properties of the operators are studied.https://www.mdpi.com/2227-7390/9/4/366index matrixintuitionistic fuzzy pairlevel operation |
| spellingShingle | Krassimir Atanassov Peter Vassilev Olympia Roeva Level Operators over Intuitionistic Fuzzy Index Matrices Mathematics index matrix intuitionistic fuzzy pair level operation |
| title | Level Operators over Intuitionistic Fuzzy Index Matrices |
| title_full | Level Operators over Intuitionistic Fuzzy Index Matrices |
| title_fullStr | Level Operators over Intuitionistic Fuzzy Index Matrices |
| title_full_unstemmed | Level Operators over Intuitionistic Fuzzy Index Matrices |
| title_short | Level Operators over Intuitionistic Fuzzy Index Matrices |
| title_sort | level operators over intuitionistic fuzzy index matrices |
| topic | index matrix intuitionistic fuzzy pair level operation |
| url | https://www.mdpi.com/2227-7390/9/4/366 |
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