Fuzzy inner product spaces and fuzzy orthogonality

Mostofian, Ehsan; Azhini, Mahdi; Bodaghi, Abasalt

doi:10.1515/tmj-2017-0034

Cited by 3 publications

(3 citation statements)

References 17 publications

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“…This notion is distinct from the others since the fuzzy inner product provides a new fuzzy norm of type Felbin. Authors in [18] proposed two new fuzzy inner product space notions and looked into some of their essential properties. Recently, L.Popa and L. Sida [19] came up with a good description for the notion of fuzzy Hilbert space.…”

Section: Introductionmentioning

confidence: 99%

Another Type of Fuzzy Inner Product Space

Sabri

Ahmed

2023

Iraqi Journal of Science

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In this paper, we generalize the definition of fuzzy inner product space that is introduced by Lorena Popa and Lavinia Sida on a complex linear space. Certain properties of the generalized fuzzy inner product function are shown. Furthermore, we prove that this fuzzy inner product produces a Nadaban-Dzitac fuzzy norm. Finally, the concept of orthogonality is given and some of its properties are proven.

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Section: Introductionmentioning

confidence: 99%

Another Type of Fuzzy Inner Product Space

Sabri

Ahmed

2023

Iraqi Journal of Science

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“…In 2017, E. Mostofian, M. Azhini and A. Bodaghi [27] presented two new concepts of fuzzy inner product spaces and investigated some of basic properties of these spaces.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Inner Product Space: Literature Review and a New Approach

Popa

Sida

2021

Mathematics

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The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta’s definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type Nădăban-Dzitac. Finally, some challenges are given.

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“…In anul 2017, E. Mostofian, M. Azhini and A. Bodaghi [21] presented two new concepts of fuzzy inner product spaces and investigated some of basic properties of these spaces.…”

Section: Introductionmentioning

confidence: 99%