Actually psychologists have identified seven basic emotions: fear, anger, joy, sadness, surprise, contempt, and disgust. "Surprise" was considered similar enough to "fear" that Pixar made one character out of them; the same goes for "contempt" and "disgust". Complexity in emotions arises from their interactions, much like how we perceive a spectrum of colors as a mixture of three primaries.

Most of the professionals in the field who saw Inside Out have praised it for getting the basics of emotion and memory right, even if it isn't super accurate. It is after all a cartoon.