Which one should I use in the sentence below?
Their intention/intentions are vital information for us to make a decision.
In this context, I want to express that what other road users intend to do is important.
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You should use intentions. "Are" is conjugated for the plural case, requiring the associated noun intention to be plural as well.
But beyond noun-verb agreement, intentions is still the best choice. If the singular form were used, it would mean that all road users share a single, unvarying intention. This is unlikely to fit the intended meaning of the sentence. The plural form allows for different intentions between different road users, as well as for a particular road user having different intentions at different points in time.