Fuzzy Norm on Fuzzy <img src=image/13427754_01.gif>-Normed Space

Abstract

In various articles, fuzzy <img src=image/13427754_06.gif>-normed space concept for <img src=image/13427754_02.gif> is constructed from fuzzy normed space which uses intuitionistic approach or <img src=image/13427754_03.gif>-norm approach concept. However, fuzzy normed space can be approached using fuzzy point too. This paper shows that fuzzy <img src=image/13427754_06.gif>-normed space for <img src=image/13427754_02.gif> can be constructed from fuzzy normed space using fuzzy point approach of fuzzy set. Furthermore, for <img src=image/13427754_07.gif>, it is also discussed how to construct fuzzy (<img src=image/13427754_05.gif>)-normed space from fuzzy <img src=image/13427754_06.gif>-normed space using fuzzy point approach. The method that can be used is as follows. From fuzzy normed space, we construct a norm function that satisfies properties of fuzzy <img src=image/13427754_06.gif>-normed, so that fuzzy <img src=image/13427754_06.gif>-normed space is derived. Conversely, from fuzzy <img src=image/13427754_06.gif>-normed space, we construct a normed function that satisfies properties of fuzzy (<img src=image/13427754_05.gif>)-normed, so that fuzzy (<img src=image/13427754_05.gif>)-normed space is obtained. Finally, we get two new theorems that state that a fuzzy <img src=image/13427754_06.gif>-normed space from any fuzzy normed space and fuzzy (<img src=image/13427754_05.gif>)-normed space for <img src=image/13427754_07.gif> from fuzzy <img src=image/13427754_06.gif>-normed space using fuzzy point of fuzzy set always can be constructed.