Abstract

The paper is concerned with fuzzy real numbers and Felbin-type fuzzy inner product spaces. At first, we study fuzzy 2-inner product and discuss a few basic results of fuzzy inner product and fuzzy $2$-inner product. The existence of fuzzy $2$-inner product is proved with the help of an example. We introduce the notion of Felbin- type fuzzy weak $n$-inner product, which is a generalized concept of fuzzy $n$-inner product. Finally, we construct an $n$-iterated fuzzy $2$-inner product and prove that it is a fuzzy weak $n$-inner product, also furnish an example of a $3$-iterated fuzzy $2$-inner product which is not a fuzzy $3$-inner product.

Keywords and Phrases

Fuzzy real numbers, fuzzy inner product, weak $n$-inner product.

A.M.S. subject classification

Primary 54A40, 03E72; Secondary 46Cxx.

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