"The underlying notions of the problem" or "The problem underlying notions"? Please consider the brevity principle too.
closed as off topic by J.R., Mehper C. Palavuzlar, RegDwighт♦ Jan 15 at 10:30
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However, choosing notions is probably less than optimal. Without a larger context, it's not easy to see why you chose that word instead of, e.g., assumptions, axioms, biases, hypotheses, ideas, or postulates.
In the second case, you have the risk of implying "The problem underlying the notions", which obviously you do not mean. Anyway it is ungrammatical.
As for the first option "The underlying notions of the problem", it is grammatical and conveys the meaning correctly. However, a better phrasing might be:
which is much more direct and places the words in their natural order.