In this article we present an algorithm to extend continuous crisp functions to fuzzy numbers using the extension principle; the functions must be monotonically increasing in some of the arguments and monotonically decreasing in the others. Then, we present two different solutions to the problem of extending inverse functions that we have called possible extension and necessary extension. Finally, using these solutions we have generated a family of intermediate extensions that let us define a parameter to measure the existence of the extended inverse functions. © 2003 Wiley Periodicals, Inc.