• Journal of the Korean Institute of Intelligent Systems
• /
• v.18 no.2
• /
• pp.268-271
• /
• 2008

In this paper, we introduce the notions of a fuzzy convergence of sequences, fuzzy Cauchy sequence and the related fuzzy completeness on a fuzzy normed linear space. And we investigate some properties relative to fuzzy normed linear spaces. In particular, we prove an equivalent conditions that a fuzzy norm defined on a ordinary normed linear space is fuzzy complete.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.2
• /
• pp.281-286
• /
• 2009

In this paper, we introduce the notion of the complete fuzzy norm on a linear space. And we consider some relations between the fuzzy completeness and ordinary completeness on a linear space.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.3
• /
• pp.597-606
• /
• 2009

In this paper, we introduce the notion of the statistically complete fuzzy norm on a linear space. And we consider some relations between the fuzzy statistical completeness and ordinary completeness on a linear space.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.4 no.2
• /
• pp.9-12
• /
• 1994

Let X, Y be normed linear spaces, and let p$_{1}$, p.sub 2/ be lower semi-continuous fuzzy norms on X, Y respectively, and have the bounded supports on X, Y respectively. In this paper, we prove that if Y is conplete, the set of all fuzzy continuous linear maps from X into Y is a fuzzy complete fuzzy normed linear space.