Fuzzy Real Pre-Hilbert Space and Some of Their Properties
In this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct space, which is a FRNS with some modification of the definition introduced by...
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University of Baghdad, College of Science for Women
2022-04-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4776 |
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| author | Mayada N. Mohammedali |
| author_facet | Mayada N. Mohammedali |
| author_sort | Mayada N. Mohammedali |
| collection | DOAJ |
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In this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct space, which is a FRNS with some modification of the definition introduced by G. Rano and T. Bag. The structure of fuzzy real Pre-Hilbert space (FRPHS) is then presented which is based on the structure of FRNS. Then, some of the properties and related concepts for the suggested space FRN such as -neighborhood, closure of the set named , the necessary condition for separable, fuzzy linear manifold (FLM) are discussed. The definition for a fuzzy seminorm on is also introduced with the prove that a fuzzy seminorm on is FRNS. The relationship between the -convergent sequence, -Cauchy sequence and -completeness is then investigated in this work. The structure of FRPHS with some important properties concerning on this space are introduced and proved. In addition, the property of orthogonality with some important properties for these spaces is included, for example the annihilator of the set . The relation between FRPHS and FRNS is investigated in the present work. Finally, after introducing the structure of FRPHS, it leads naturally to the definition of the most important class of FRPHS, namely the fuzzy real Hilbert space (FRHS).
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| format | Article |
| id | doaj-art-b9d7cc970a0d46fbb9489d7e9d80a5fd |
| institution | Kabale University |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2022-04-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-b9d7cc970a0d46fbb9489d7e9d80a5fd2025-08-20T03:57:43ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862022-04-0119210.21123/bsj.2022.19.2.0313Fuzzy Real Pre-Hilbert Space and Some of Their PropertiesMayada N. Mohammedali0Department of Applied Sciences, University of Technology, Baghdad, Iraq. In this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct space, which is a FRNS with some modification of the definition introduced by G. Rano and T. Bag. The structure of fuzzy real Pre-Hilbert space (FRPHS) is then presented which is based on the structure of FRNS. Then, some of the properties and related concepts for the suggested space FRN such as -neighborhood, closure of the set named , the necessary condition for separable, fuzzy linear manifold (FLM) are discussed. The definition for a fuzzy seminorm on is also introduced with the prove that a fuzzy seminorm on is FRNS. The relationship between the -convergent sequence, -Cauchy sequence and -completeness is then investigated in this work. The structure of FRPHS with some important properties concerning on this space are introduced and proved. In addition, the property of orthogonality with some important properties for these spaces is included, for example the annihilator of the set . The relation between FRPHS and FRNS is investigated in the present work. Finally, after introducing the structure of FRPHS, it leads naturally to the definition of the most important class of FRPHS, namely the fuzzy real Hilbert space (FRHS). https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4776Fuzzy Inner Product (FIP), Fuzzy Norm (FN), Fuzzy Real Hilbert Space, Fuzzy Real Normed Space, Fuzzy Orthogonality. |
| spellingShingle | Mayada N. Mohammedali Fuzzy Real Pre-Hilbert Space and Some of Their Properties مجلة بغداد للعلوم Fuzzy Inner Product (FIP), Fuzzy Norm (FN), Fuzzy Real Hilbert Space, Fuzzy Real Normed Space, Fuzzy Orthogonality. |
| title | Fuzzy Real Pre-Hilbert Space and Some of Their Properties |
| title_full | Fuzzy Real Pre-Hilbert Space and Some of Their Properties |
| title_fullStr | Fuzzy Real Pre-Hilbert Space and Some of Their Properties |
| title_full_unstemmed | Fuzzy Real Pre-Hilbert Space and Some of Their Properties |
| title_short | Fuzzy Real Pre-Hilbert Space and Some of Their Properties |
| title_sort | fuzzy real pre hilbert space and some of their properties |
| topic | Fuzzy Inner Product (FIP), Fuzzy Norm (FN), Fuzzy Real Hilbert Space, Fuzzy Real Normed Space, Fuzzy Orthogonality. |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4776 |
| work_keys_str_mv | AT mayadanmohammedali fuzzyrealprehilbertspaceandsomeoftheirproperties |