I recently updated the indices through November 2015. As the figure below shows, short-horizon inflation uncertainty reached a historical maximum in February 2009, but has since fallen and remained relatively steady in the last two years. Consumers are less uncertain about longer-run than shorter- run inflation since around 1990. This makes sense if at least some consumers have anchored expectations, i.e. they are fairly certain about what will happen with inflation over the longer run, even if they expect it to fluctuate in the shorter run.
In my paper, I interpreted the decline of long-run consumer inflation uncertainty over the 1980s as a result of improved anchoring during and following the Volcker disinflation, but noted the apparent lack of improvement since the mid-90s, despite the Fed's efforts to improve its communication strategy and better anchor expectations. With an extra year of data, it looks like long-run inflation uncertainty may have actually declined, if only slightly, in the last few years. Still, that doesn't mean that consumers' expectations are strongly anchored, as I show in another working paper (which Kumar et al. follow up for New Zealand with similar results).