Fuzzy logic, introduced in 1965 by Lotfi A. Zadeh, is a computational paradigm that departs from the rigid true/false dichotomies of classical Boolean logic. It is designed to model human-like reasoning by mathematically representing and processing imprecise and vague information. The core principle of fuzzy logic is the concept of “degrees of truth,” where a proposition’s truth value can be any real number between 0.0 (absolute falseness) and 1.0 (absolute truth).

This approach is founded on Fuzzy Set Theory, which allows elements to have partial membership in a set. This degree of membership is defined by a Membership Function, which is central to characterizing the fuzziness of any given concept. The practical application of fuzzy logic involves two critical processes: Fuzzification, the conversion of precise, crisp input data into fuzzy sets, and Defuzzification, the conversion of fuzzy output sets back into a single, crisp value that can be used to actuate a system.

The decision-making engine of a fuzzy logic system is the Fuzzy Inference System (FIS). The FIS utilizes a knowledge base, consisting of a database of membership functions and a rule base of IF-THEN statements, to perform approximate reasoning and deduce outputs. The Mamdani and Takagi-Sugeno models are the two primary methods for implementing these inference systems.

Fuzzy logic has demonstrated immense utility, most notably in the domain of control systems (Fuzzy Logic Control or FLC). FLCs are known for their robustness and cost-effectiveness, finding widespread use in consumer electronics, automotive systems like anti-braking systems, and complex industrial processes. Beyond control, fuzzy logic is applied extensively in fields such as finance for market prediction, medical diagnostics, pattern recognition, and artificial intelligence, where it synergizes with neural networks to create adaptive, intelligent systems.