Well, let me start by saying this is nothing strange or special. It's what you do all the time whenever you need to resolve an ambiguity. You just take the cloud of features that makes up the definition of a conceptual category, compare it to the features you observe on a physical thing, and see how well they match.
So (to blatantly rip off my example from someone else's blog), if you see something skittering through your kitchen out of the corner of your eye, and you think "is that a rat?" you take a better look at it (after pausing the TiVo) and compare: it's a small rodent, but look, it's got the wrong kind of tail. It's a squirrel, not a rat. The vast majority of the time, the matching is easy and obvious, so fuzziness doesn't matter.
Now, consider a fuzzier case: there's a big juniper in your yard. Is it a bush, or is it a tree? It's hard to tell. We could probably make a determination, but we don't need to if all we want to do is trim the thing; whether it's a tree or a bush is irrelevant. So we can handle fuzziness without addressing it in some cases.
In other cases, we have to resolve the ambiguity in order to make a decision or some such. And the need provides important context for the resolution, because if we didn't have a need to resolve it, we could just leave it ambiguous and address it in its naturally fuzzy state, right?
The stack of Hamlet pages on the coffeetable can be matched against any number of patterns. The ambiguity in matching it against the "book" pattern only matters if the question "is it a book?" has somehow been asked, implicitly or explicitly, in a way that does not allow "sort of" as a valid answer.
[Aside: I'm starting to think that the correct answer to many (most?) philosophical conundrums is "that's a bad question, because it depends on context that hasn't been provided".]
So let's consider this situation: Alan says to Bob "hey, would you go and grab the books off my coffeetable?" Bob sees two regular books and a stack of loose pages. Did Alan mean to grab that, too? Is that "a book"? The answer depends on context. If Bob knows that Alan is editing a manuscript, he might decide yes. If Alan is shelving things on a bookshelf, he might decide no. It depends on the circumstances surrounding the question.
If the immediate circumstances don't help, then Bob will start pulling on broader context, drawing on his personal understanding of the universe. If he works at a bookstore, the aspect of books as "things that are bound" comes more easily to mind for him, and he decides that the unbound pages are not a book. If he's been sorting through letters and forms all day, the aspect that is "a lengthy collection of text" might be prominent, and he decides yes, it is.
Now, in neither case has the fuzziness gone away. All that's happened is that Bob was constrained to deal with a borderline case in an all-or-nothing way, so he evaluated it in that context to determine whether the mapping between physical object and informational object held. When exterior context was insufficient to resolve the ambiguity, he called on his mental model of the universe to get more context so that he could make a subjective decision. In a different context, he might come to a different decision. A different person in the same context might come to a different decision.
The fuzziness remains, it's just a way of treating it as if resolved in a particular context.