General approximation of fuzzy numbers by F-transform

In this paper we will prove that in most of the cases the extended inverse fuzzy transform preserves the quasi-concavity of a fuzzy number and hence it can be used to generate fuzzy numbers by approximating the restriction of the membership function to its support. In the case of continuous fuzzy numbers with cores containing more than one element, the rate of uniform convergence is of linear type and the same holds when we approximate the important characteristics of a fuzzy number such as the value or the ambiguity. Moreover we have the preservation of the support and the convergence of the core which in addition can be determined precisely. In the case of continuous fuzzy numbers with one-element core, it is in general necessary to normalize the approximation, but the support is preserved again and the core can be determined exactly in this case too. Moreover, the approximations have again linear rate of uniform convergence.