A membership function is a mathematical tool used in fuzzy logic to define how each element in a given set is associated with a degree of membership. It assigns a value between 0 and 1 to each element, indicating its level of belonging to a fuzzy set. For example, in the fuzzy set of tall people, a person who is 6 feet tall might have a membership value of 0.8, while someone who is 5 feet 5 inches might have a value of 0.3. Membership functions can take various shapes, such as triangular, trapezoidal, or Gaussian, depending on how the fuzzy set is defined. They are essential in applications like fuzzy control systems and artificial intelligence, where they help in making decisions based on imprecise or uncertain information. By using membership functions, systems can better handle real-world complexities and provide more nuanced outputs.