Fuzzy Logic: Theory, Mathematics and Applications

Fuzzy logic was introduced by Lotfi A. Zadeh in 1965 as a way to move past the strict true/false boundaries of classical logic. Instead of forcing every statement into one of two categories, it allows degrees of truth anywhere between 0 and 1. This paper traces the full arc of fuzzy logic from Zadeh's original idea through the major mathematical tools that followed, including membership functions, fuzzy operators, inference systems and defuzzification methods. It also covers modern extensions such as type-2 fuzzy sets and intuitionistic fuzzy sets, and surveys applications in engineering, medicine, finance and autonomous systems.