Fuzzy Sets

Fuzzy sets are groups whose components can have vague and varying degrees of membership. Fuzzy theory differs from classical theory in that there can be a vague definition for membership to a set instead of the in or out viewpoint of classical theory. This is best illustrated using a metaphor.

A person has a house where their bedroom connects to the living room. When they are in their bedroom they are in the set "bedroom" and when they are in the living room they are in the set "living room." But what if they are in the doorway? Classical theory insists that to belong to a set the person would need to be entirely in the bedroom or entirely in the living room.

Fuzzy logic allows for the person to be included in a set in a vague way or by varying degrees. So the person could be mostly in the bedroom and be included in the "bedroom" set. Fuzzy set logic is used in psychology for modeling concepts. Scientists have used it in a combination of natural and social sciences to make models about how humans interact with the environment. In cognitive psychology fuzzy logic is used in the formation of cognitive maps, which are mental representations of our surroundings that help an individual perceive, store, and recall information about our environment.

We use fuzzy logic to form a cognitive map in which relations between different sets of a mental landscape interact with each other and used in relation to one another.