Extension principles enable to extend maps (or morphisms) between
basic structures to maps between derived structures. A well-known
example is the Zadeh’s extension principle, which enables to extend
any map f: A -> B to a map between corresponding sets F(A), F(B) of
fuzzy sets. On the other hand, extension principles are frequently
defined “ad hoc”, i.e. instead of defining properties of extended
maps, direct formulas for extended maps are presented, without any
explanation for those choices. In this talk general properties of
extension principles will be discussed. Special attention will be
devoted to the case, when derived structures will represent “fuzzy
objects” defined on basic structures.