Inner Product over Fuzzy Matrices
The purpose of this study was to introduce the inner product over fuzzy matrices. By virtue of this definition, α-norm is defined and the parallelogram law is proved. Again the relative fuzzy norm with respect to the inner product over fuzzy matrices is defined. Moreover Cauchy Schwarz inequality, P...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2016/6521893 |
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| author | A. Nagoor Gani K. Kannan A. R. Manikandan |
| author_facet | A. Nagoor Gani K. Kannan A. R. Manikandan |
| author_sort | A. Nagoor Gani |
| collection | DOAJ |
| description | The purpose of this study was to introduce the inner product over fuzzy matrices. By virtue of this definition, α-norm is defined and the parallelogram law is proved. Again the relative fuzzy norm with respect to the inner product over fuzzy matrices is defined. Moreover Cauchy Schwarz inequality, Pythagoras, and Fundamental Minimum Principle are established. Some equivalent conditions are also proved. |
| format | Article |
| id | doaj-art-73621aecaa624e9b93939db018b6c0b3 |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-73621aecaa624e9b93939db018b6c0b32025-08-20T02:06:16ZengWileyJournal of Mathematics2314-46292314-47852016-01-01201610.1155/2016/65218936521893Inner Product over Fuzzy MatricesA. Nagoor Gani0K. Kannan1A. R. Manikandan2P.G & Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli 620 020, IndiaDepartment of Mathematics and Statistics, University of Jaffna, Jaffna, Sri LankaDepartment of Mathematics, Sengunthar Arts and Science College, Neikkarapatti, Tiruchengode, Tamil Nadu 637205, IndiaThe purpose of this study was to introduce the inner product over fuzzy matrices. By virtue of this definition, α-norm is defined and the parallelogram law is proved. Again the relative fuzzy norm with respect to the inner product over fuzzy matrices is defined. Moreover Cauchy Schwarz inequality, Pythagoras, and Fundamental Minimum Principle are established. Some equivalent conditions are also proved.http://dx.doi.org/10.1155/2016/6521893 |
| spellingShingle | A. Nagoor Gani K. Kannan A. R. Manikandan Inner Product over Fuzzy Matrices Journal of Mathematics |
| title | Inner Product over Fuzzy Matrices |
| title_full | Inner Product over Fuzzy Matrices |
| title_fullStr | Inner Product over Fuzzy Matrices |
| title_full_unstemmed | Inner Product over Fuzzy Matrices |
| title_short | Inner Product over Fuzzy Matrices |
| title_sort | inner product over fuzzy matrices |
| url | http://dx.doi.org/10.1155/2016/6521893 |
| work_keys_str_mv | AT anagoorgani innerproductoverfuzzymatrices AT kkannan innerproductoverfuzzymatrices AT armanikandan innerproductoverfuzzymatrices |