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

Taechang Byun, Ji Eun Lee, Keun Young Lee and Jin Hee Yoon
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Taechang Byun: Faculty of Mathematics and Statistics, Sejong University, Seoul 05006, Korea
Ji Eun Lee: Faculty of Mathematics and Statistics, Sejong University, Seoul 05006, Korea
Keun Young Lee: Faculty of Mathematics and Statistics, Sejong University, Seoul 05006, Korea
Jin Hee Yoon: Faculty of Mathematics and Statistics, Sejong University, Seoul 05006, Korea

Mathematics, 2020, vol. 8, issue 4, 1-7

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.

Keywords: fuzzy inner product space; Cauchy–Schwartz inequality; linearity; positive-definiteness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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