Fuzzy Inner Product and Fuzzy Norm of Hyperspaces

Abstract

We introduce and study fuzzy (co-)inner product and fuzzy<br />(co-)norm of hyperspaces. In this regard by considering the notion<br />of hyperspaces, as a generalization of vector spaces, first we will<br />introduce the notion of fuzzy (co-)inner product in<br /> hyperspaces and will apply it to formulate the notions of<br />fuzzy (co-)norm and fuzzy (co-)orthogonality in hyperspaces. In<br />particular, we will prove that to every fuzzy hyperspace there is an associated<br />unique fuzzy inner product in a natural way.