A fuzzy set is a mathematical concept that extends traditional set theory by allowing elements to have varying degrees of membership. Unlike classical sets, where an element either belongs or does not belong, fuzzy sets assign a membership value between 0 and 1. This approach is useful for dealing with uncertainty and vagueness in real-world situations, such as in artificial intelligence and decision-making processes. In a fuzzy set, for example, the concept of "tall people" can include individuals with heights ranging from 5 to 7 feet, with each height assigned a specific membership value. This flexibility enables more nuanced classifications, making fuzzy sets applicable in fields like control systems and data analysis.