fuzzylogic

Fuzzy logic is a form of logic for reasoning under uncertainty. Introduced by Lotfi Zadeh in 1965, it extends classical Boolean logic by allowing truth values between 0 and 1. Rather than crisp true or false, statements can be partially true, enabling reasoning with vague concepts. The framework relies on fuzzy sets, where elements have degrees of membership defined by membership functions, and on linguistic variables that express everyday terms such as tall, warm, or likely.

Core components include fuzzy sets, membership functions, linguistic variables, and a rule base. Inference combines rules with fuzzy operators such as min and max during conjunction and disjunction, producing a fuzzy output that is then defuzzified to a crisp value. Common paradigms include Mamdani and Takagi–Sugeno, with applications in control systems, consumer electronics, and pattern recognition.

Fuzzy logic is distinct from probability theory. It addresses vagueness and human-style reasoning rather than randomness. Its strengths lie in translating subjective judgments and modeling gradual transitions, but its design can be subjective due to chosen membership functions, and large systems may incur computational overhead. Critics note potential issues with interpretability and the lack of a universal theoretical foundation.

Fuzzy logic underpins a wide range of applications, including temperature and speed control, image processing, and decision support. It also forms the basis of hybrid methods that combine fuzzy reasoning with neural networks and other AI techniques, continuing to influence research and practical engineering.