Approximations of fuzzy numbers by step type fuzzy numbers

In this paper, the problems of approximations in membership functions space are studied. Firstly, the concept of simple fuzzy numbers is defined, which is a special kind of fuzzy numbers with simple structure, and give the expressions of the membership function of thus fuzzy numbers. Then, we prove that a fuzzy set of real number field R is a simple fuzzy number if and only if it is a normal step type fuzzy set, and obtain a result of that simple fuzzy number space is dense in the fuzzy number space with respect to some metric. And then, we give two theorems about approximations of fuzzy number membership functions by using simple fuzzy number membership functions. At last, we investigate the properties of approximation operators given by us.