Is it unwise to pick an old field of research in maths to write a PhD thesis about?
If you pick an overly-trendy area there is a chance that it will be easier to get a Ph.D. in that area but that many mathematicians will be less than impressed by the resulting degree. For example, "fuzzy" is (or has been?) a trendy concept. There is almost a template for getting a Ph.D. in it (albeit one which is getting harder to apply by sheer competition): pick some topic in pure mathematics for which there doesn't yet exist a fuzzy version (for an example the exact phrase "fuzzy symmetry group" has only 4 Google hits). Learn the classical theory. Fuzzify it: whenever you see the word "set" replace it with "fuzzy set". Prove something -- which with lack of competition shouldn't be all that hard. Anticipating the question as to why anyone should care, hand-wave about potential applications to artificial intelligence. Voila! You have a dissertation (I am exaggerating a bit, this is of course easier said than done, and a successful fuzzification will involve more than simply replacing sets by fuzzy sets).

Now I don't deny that the core concepts of fuzzy logic and fuzzy set theory have a great deal of mathematical depth, and that much of the fuzzification of classical pure mathematics has been well-motivated. Still, it seems likely that much of it has been done just because it was low-hanging fruit for somebody who wanted to write a dissertation or paper. I am instinctually skeptical of the value of a paper when it contains the word "fuzzy" in the title. I won't dogmatically reject it, but I will need some convincing as to its value. If your dissertation has a trendy buzz-word but otherwise seems unmotivated, you might meet with similar skepticism.