  In this paper we consider how to use the convolution method to construct
approximations, which consist of fuzzy numbers sequences with good properties,
for a general fuzzy number. It shows that this convolution method can generate
differentiable approximations in finite steps for fuzzy numbers which have
finite non-differentiable points. In the previous work, this convolution method
only can be used to construct differentiable approximations for continuous
fuzzy numbers whose possible non-differentiable points are the two endpoints of
1-cut. The constructing of smoothers is a key step in the construction process
of approximations. It further points out that, if appropriately choose the
smoothers, then one can use the convolution method to provide approximations
which are differentiable, Lipschitz and preserve the core at the same time.
