*Article* **Fuzzy Inner Product Space: Literature Review and a New Approach**

**Lorena Popa and Lavinia Sida \***

> Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Dragoi 2, RO-310330 Arad, Romania; lorena.popa@uav.ro **\***

Correspondence: lavinia.sida@uav.ro

**Abstract:** The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the alreadyexistent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta's definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type N˘ad˘aban-Dzitac. Finally, some challenges are given.

**Keywords:** fuzzy Hilbert space; fuzzy inner product; fuzzy norm

**MSC:** 46A16; 46S40

## **Citation:** Popa, L.; Sida, L. Fuzzy Inner Product Space: Literature Review and a New Approach. *Mathematics* **2021**, *9*, 765. https://doi.org/10.3390/ math9070765

Academic Editor: Basil Papadopoulos

Received: 22 February 2021 Accepted: 27 March 2021 Published: 1 April 2021

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