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Absence of Non-Trivial Fuzzy Inner Product Spaces and the Cauchy–Schwartz Inequality

Author

Listed:
  • Taechang Byun

    (Faculty of Mathematics and Statistics, Sejong University, Seoul 05006, Korea
    These authors contributed equally to this work.)

  • Ji Eun Lee

    (Faculty of Mathematics and Statistics, Sejong University, Seoul 05006, Korea
    These authors contributed equally to this work.)

  • Keun Young Lee

    (Faculty of Mathematics and Statistics, Sejong University, Seoul 05006, Korea
    These authors contributed equally to this work.)

  • Jin Hee Yoon

    (Faculty of Mathematics and Statistics, Sejong University, Seoul 05006, Korea
    These authors contributed equally to this work.)

Abstract

First, we show that the non-trivial fuzzy inner product space under the linearity condition does not exist, which means a fuzzy inner product space with linearity produces only a crisp real number for each pair of vectors. If the positive-definiteness is added to the condition, then the Cauchy–Schwartz inequality is also proved.

Suggested Citation

  • Taechang Byun & Ji Eun Lee & Keun Young Lee & Jin Hee Yoon, 2020. "Absence of Non-Trivial Fuzzy Inner Product Spaces and the Cauchy–Schwartz Inequality," Mathematics, MDPI, vol. 8(4), pages 1-7, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:571-:d:344478
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