The review analyses the fundamental principles which Artificial Intelligence should be based on in order to imitate the realistic process of taking decisions by humans experiencing emotions. Two approaches are considered, one based on quantum theory and the other employing classical terms. Both these approaches have a number of similarities, being principally probabilistic. The analogies between quantum measurements under intrinsic noise and affective decision making are elucidated. It is shown that cognitive processes have many features that are formally similar to quantum measurements. This, however, in no way means that for the imitation of human decision making Affective Artificial Intelligence has necessarily to rely on the functioning of quantum systems. The analogies between human decision making and quantum measurements merely demonstrate formal common properties in their functioning. It is in this sense that one has to understand quantum operation of Artificial Intelligence. Appreciating the common features between quantum measurements and decision making helps for the formulation of an axiomatic approach employing only classical notions. Artificial Intelligence, following this approach, operates similarly to humans, by taking into account the utility of the considered alternatives as well as their emotional attractiveness. Affective Artificial Intelligence, whose operation takes account of the cognition-emotion duality, avoids numerous behavioural paradoxes of traditional decision making. A society of intelligent agents, interacting through the repeated multistep exchange of information, forms a network accomplishing dynamic decision making based on the evaluation of utility and affected by the emotional attractiveness of alternatives. The considered intelligent networks can characterize the operation of either a human society of affective decision makers, or the brain composed of neurons, or a typical probabilistic network of an artificial intelligence.