We present in this paper a finitary approach to the concept of fuzzy comput
ability. On this basis we define the class FR of fin-recursive W-functions.
We prove that FR is a strict subset of the class of W-functions with recur
sive graph, as defined by Gerla. We show that it is possible to generate th
e class FR by means of programs written in the language XL. (C) 2001 Elsevi
er Science B.V. All rights reserved.