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Fuzzy Inner Product Space: Literature Review and a New Approach

Author

Listed:
  • Lorena Popa

    (Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Dragoi 2, RO-310330 Arad, Romania)

  • Lavinia Sida

    (Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Dragoi 2, RO-310330 Arad, Romania)

Abstract

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.

Suggested Citation

  • Lorena Popa & Lavinia Sida, 2021. "Fuzzy Inner Product Space: Literature Review and a New Approach," Mathematics, MDPI, vol. 9(7), pages 1-9, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:765-:d:528487
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    References listed on IDEAS

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    1. Bînzar, Tudor & Pater, Flavius & Nădăban, Sorin, 2020. "Fuzzy bounded operators with application to Radon transform," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Goudarzi, M. & Vaezpour, S.M. & Saadati, R., 2009. "On the intuitionistic fuzzy inner product spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1105-1112.
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    Cited by:

    1. Sorin Nădăban, 2022. "Fuzzy Logic and Soft Computing—Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921–2017)," Mathematics, MDPI, vol. 10(17), pages 1-3, September.

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