This paper deals with the Generalized Extension Principle (GEP) applied to fuzzy numbers. Some concepts are introduced in order to allow the extension of real functions with restricted domain, including the notion of \(\varphi \) -extension. To formalize the extension of real functions to maps whose both domain and codomain are subsets of the set of fuzzy numbers, the definition of fuzzy number function is presented. The objective is to generate fuzzy number functions through the \(\varphi \) -extension of real number functions. This requires some restrictions to the aggregation functions used to generate the extension. These restrictions are studied in detail. The aggregation functions that generate fuzzy number functions are characterized as the ones with 0 as annihilator and upper semi-continuous.
