  We explore the structure of non-redundant and minimal sets consisting of
graded if-then rules. The rules serve as graded attribute implications in
object-attribute incidence data and as similarity-based functional dependencies
in a similarity-based generalization of the relational model of data. Based on
our observations, we derive a polynomial-time algorithm which transforms a
given finite set of rules into an equivalent one which has the least size in
terms of the number of rules.
