I recently got an unsolicited email advertising a questionable-looking mathematics journal. Upon investigation, it looks pretty shady: page charges, manuscripts to be submitted in Microsoft Word (legitimate math journals always use LaTeX), overbroad scope, and a promise for peer review within 2 months (unreasonably short for mathematics).
And in its three years of operation, one particular author has been published in it three times, including an "elementary" proof of Fermat's Last Theorem, and another paper that appears to be a proof of a statement for which an explicit numerical counterexample is known. (Interestingly, it appears the same author has also published a proof of the Goldbach conjecture in a journal with a nearly identical name from another publisher, and it's indexed in MathSciNet, and has also apparently settled the Twin Primes and Collatz conjectures!
(Since the preceding paragraph may not make any sense to non-mathematicians, let me say: this is roughly the equivalent of a physics journal publishing a paper that claims to have achieved time travel with household materials. I should note that the journal has a subscription fee (which I have no intention of paying), so I can't actually read the articles in question; but their abstracts are pretty damning.)
However, the journal's editorial board includes some names from reputable institutions; people with many publications in high-quality journals. (There are many other names from institutions I know nothing about.) Giving them the benefit of the doubt, it's entirely possible that they are not paying attention to what the journal is doing, or they agreed to be editors without checking on the journal, or even that they have been listed without their knowledge (this has been known to happen).
Is it appropriate to try to inform these editors what's happening in their names? If so, how can I do it tactfully?
On the one hand, if someone was using my name on a shady journal, I'd want to know. On the other hand, I don't want to offend or embarrass them by just sending an email saying "this journal you edit is crap". It's even possible that they somehow approve of the journal (e.g. they have a philosophy that the world generally needs more journals and fewer barriers to publication), in which case, I fear no good can come of me criticizing it to them.
Edit: Since some people have expressed interest in knowing what the journal is, it is Pioneer Journal of Algebra, Number Theory and its Applications. But my question isn't really about this specific journal (there are many more like it), but rather how to approach this issue in general.