Absence of Non-Trivial Fuzzy Inner Product Spaces and the Cauchy–Schwartz Inequality - Taechang Byun; Ji Eun Lee; Keun Young Lee; Jin Hee Yoon (Mathematics, 2020)
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.