Another Type of Fuzzy Inner Product Space

Abstract

In this paper, we generalize the definition of fuzzy inner product space that is introduced by Lorena Popa and Lavinia Sida on a complex linear space. Certain properties of the generalized fuzzy inner product function are shown. Furthermore, we prove that this fuzzy inner product produces a Nadaban-Dzitac fuzzy norm. Finally, the concept of orthogonality is given and some of its properties are proven.

On α ̌–φ ̆-Fuzzy Contractive Mapping in Fuzzy Normed Space

“…Functional analysis is one of the most important areas of contemporary mathematics. It plays an essential role in the theory of differential equations, representation theory, and probability, as well as in the study of many different properties of different spaces, such as metric space, Hilbert space, Banach space, and others see references [1][2][3][4] . Fuzzy sets were first proposed by Zadeh in 1965.…”