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Open AccessArticle

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

Faculty of Mathematics and Statistics, Sejong University, Seoul 05006, Korea
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(4), 571; https://doi.org/10.3390/math8040571
Received: 10 February 2020 / Revised: 6 April 2020 / Accepted: 6 April 2020 / Published: 11 April 2020
(This article belongs to the Special Issue Fuzziness and Mathematical Logic )
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. View Full-Text
Keywords: fuzzy inner product space; Cauchy–Schwartz inequality; linearity; positive-definiteness fuzzy inner product space; Cauchy–Schwartz inequality; linearity; positive-definiteness
MDPI and ACS Style

Byun, T.; Lee, J.E.; Lee, K.Y.; Yoon, J.H. Absence of Non-Trivial Fuzzy Inner Product Spaces and the Cauchy–Schwartz Inequality. Mathematics 2020, 8, 571.

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