What is intuition? The Wikipedia entry says “Intuition is the ability to acquire knowledge without inference or the use of reason.”
Intuition is something that enables you act without using inference (or knowledge gained from inference) to help you decide upon the right course of action.
So, an intuitive course of action is determined by your feelings – those proverbial feelings in the pit of one’s stomach – and not by conscious reasoning.
However, intuition is not the only tool that decisions come to be based on.
Instead of relying on intuition, a human being can base his or her decisions on logic.
Logic-based (or you might call it rule-based) decision-making is a method of proceeding from a number of premises and eventually arriving at a decision/conclusion (or a course of action) through inference.
So, there seems to be a dichotomy in decision making: intuitive and logic-based.
In AI, there seems to be a similar dichotomy. One area of research in AI deals with planners and inference engines which are clearly logic/rule based.
Then there is an area of research called Machine Learning (ML) which deals with the study of systems that can be trained to recognize patterns.
You first need to train ML systems on examples of decisions made under certain circumstances and the rewards obtained as a result. After sufficient training, the ML systems ought to by themselves be able to take decisions when presented with a set of circumstances, even if it is a set of circumstances they have never encountered before.
Some ML systems are rule-based. Decision tree classifiers are a good example.
But there are some ML systems that seem to have a method of operation that resembles intuition.
One example is ANNs (Artificial Neural Networks).
Another is a family of ML systems that are statistical in nature and are known as Discriminative Models.
There are also systems that are a combination of both. They are called Probabilistic Graphical Models. These seem to use what closely resembles a combination of intuition and inference.