The system already does support approximate match for a list of values entity, but it all depends on how the synonyms are specified.
If each synonym is enclosed in double quotes then that is taken as an exact match - all words must be present and in that order.
But if a synonym is not quoted then the system will allow the user to be vague or less exact in their response. If the system judges that to be a clear indication then that choice is taken, or if it is ambiguous then a limited set of choices will be represented.
Also see Facing ambiguity issue with List of Values entity type