Mathematics and Statistics Vol. 10(5), pp. 1075 - 1080
DOI: 10.13189/ms.2022.100517
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Fuzzy Norm on Fuzzy -Normed Space

Mashadi ¹, Abdul Hadi ¹, Sukono ^2,*
1 Department of Mathematics, Faculty of Mathematics and Natural Sciences, Riau University, Indonesia
² Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjajaran, Indonesia

ABSTRACT

In various articles, fuzzy -normed space concept for is constructed from fuzzy normed space which uses intuitionistic approach or -norm approach concept. However, fuzzy normed space can be approached using fuzzy point too. This paper shows that fuzzy -normed space for can be constructed from fuzzy normed space using fuzzy point approach of fuzzy set. Furthermore, for , it is also discussed how to construct fuzzy ()-normed space from fuzzy -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 -normed, so that fuzzy -normed space is derived. Conversely, from fuzzy -normed space, we construct a normed function that satisfies properties of fuzzy ()-normed, so that fuzzy ()-normed space is obtained. Finally, we get two new theorems that state that a fuzzy -normed space from any fuzzy normed space and fuzzy ()-normed space for from fuzzy -normed space using fuzzy point of fuzzy set always can be constructed.

KEYWORDS
Norm Space, -Normed Space, Fuzzy Normed Space, Fuzzy -Normed Space

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mashadi , Abdul Hadi , Sukono , "Fuzzy Norm on Fuzzy -Normed Space," Mathematics and Statistics, Vol. 10, No. 5, pp. 1075 - 1080, 2022. DOI: 10.13189/ms.2022.100517.

(b). APA Format:
Mashadi , Abdul Hadi , Sukono (2022). Fuzzy Norm on Fuzzy -Normed Space. Mathematics and Statistics, 10(5), 1075 - 1080. DOI: 10.13189/ms.2022.100517.