Systems are modeled in Reliability Theory by means of Structure Functi
ons, which show how the system state of performance depends on the sta
te of all its components. In this paper we consider that the space of
states allowed for both the system and its components is an appropriat
e family of fuzzy numbers. Basic concepts in classical crisp binary an
d multistate models in Reliability Theory are in this way generalized.
Some particular consequences relative to component importance are als
o analyzed.