  A class of integer-valued functions defined on the set of ideals of an
integral domain $R$ is investigated. We show that this class of functions,
which we call ideal valuations, are in one-to-one correspondence with countable
descending chains of finite type, stable semistar operations with largest
element equal to the $e$-operation. We use this class of functions to recover
familiar semistar operations such as the $w$-operation and to give a solution
to a conjecture by Chapman and Glaz when the ring is a valuation domain.
