This document defines and explains key concepts in fuzzy set theory, including fuzzy complements, unions, and intersections. It begins with an introduction to fuzzy sets as a generalization of classical sets that allows for gradual membership rather than binary membership. Membership functions assign elements a value between 0 and 1 indicating their degree of belonging to a set. The document then provides definitions and properties of fuzzy complements, unions, intersections, and other related concepts. It concludes with examples of applications of fuzzy set theory such as traffic monitoring systems, appliance controls, and medical diagnosis.