Parameterized (in)approximability of subset problems

We discuss approximability and inapproximability in FPT-time for a large class of subset problems   where a feasible solution SS is a subset of the input data. We introduce the notion of intersective approximability that generalizes the one of safe approximability introduced in Guo et al. (2011) and show strong parameterized inapproximability results for many of the subset problems handled.