“Intuition” is often used synonymously with making a judgment based purely on feelings without dispassionate, logical deliberation. But it’s more useful to recognize intuition and feeling as distinct functions. We may have intuitions about relationships and abstract concepts alike.
Making judgments from feeling is a different thing and a rational process insofar as it’s reasonable. For instance, using our feelings to interpret a romantic gesture or determine the time and manner to break bad news to our boss is as rational and appropriate as modeling how much weight a bridge can hold with mathematics or making a budget using a spreadsheet.