Based on metrics d_i defined on reference [1] we consider the topological properies of fuzzy valued metric spaces(M[0,1],d i)(i=2,3),obtain the following conclusion:(M[0,1],d i)(i=2,3) are complete,connected,compact and separable metric spaces.

We introduce three kinds of metrics d i(i=1, 2, 3) in Fuzzy valued space M[0, 1], and consider the topological properties of fuzzy valued metric spaces( M [0, 1], d i)(i=1, 2, 3) .

Specifically, existence, uniqueness and continuous dependence of fuzzy solutions for the fuzzy retarded integro-differential equation u·(t)=∫~t_0g(t,s,u(s))ds+f(t,x_t), where E~n is the set of all upper semi-continuous convex normal fuzzy numbers with bounded α-level set, f,g is continuous functions, are establish via Banach fixed-point theorem and the property of metric space of fuzzy set.

Some properties on WF-fuzzy metric spaces(Ⅱ);

Thus, the fixed point theorems for mappings of contractive type and locally contractive type on WF fuzzy metric spaces are established.

n-dimensional Fuzzy Metric Space and Its Completeness;

In this paper, we obtain some common fixed point theorems under the condition of R-weakly commuting in fuzzy metric spaces and then extend these results to fuzzy 2 and 3-metric spaces.

This paper discusses some related concepts in fuzzy metric spaces, gives several important fixed point theorems of φcontrictive mappings with C property and non-expansive mappings in complete fuzzy metric spaces.