The notions of fuzzy vector spaces and fuzzy topological vector spaces were introduced in Katsaras and Liu (1977). These ideas were modified by Katsaras (1981), and in (1984) Katsaras defined the fuzzy norm on a vector space. In (1991) Krishna and Sarma discussed the generation of a fuzzy vector topology from an ordinary vector topology on vector spaces. Also Krishna and Sarma (1992) observed the convergence of sequence of fuzzy points. Rhie et al. (1997) Introduced the notion of fuzzy Cauchy sequence of fuzzy points and fuzzy completeness.
Throughout this paper and means fuzzy topological spaces (fts). The notions Cl (A) will stand for the fuzzy closure of a fuzzy set A in a fts . Support of a fuzzy set A in will be denoted by S (A). The fuzzy sets in taking on respectively the constant value 0 and 1 are denoted by and respectively.
In this paper, we first observe a type of the convergence of sequences as an analogy of Bag and Samanta (2003) in a fuzzy normed linear space. Secondly, we introduce the notion of a complete fuzzy norm, using the convergence of a sequence of a linear space. And we consider some relations between the fuzzy completeness and the ordinary completeness on a linear space.
Definition 1.1: [4] For two fuzzy subsets and of , the fuzzy subset is defined by
And for a scalar of and a fuzzy subset of , the fuzzy subset is defined by
Definition 1.2: [2] is said to be
Convex if
Balanced if
Absorbing if
Definition 1.3: [2] Let be a topological space and