Two main trends are mentioned: the fuzzy set theory and the fuzzy logic. Both build upon set theory and logic, respectively. Three features distinguish the approaches: (1) the use of so called linguistic variables, instead of or together with numeric variables; (2) the use of fuzzy conditional statements to represent simple relations between variables; and (3) the characterization of complex relations by fuzzy algorithms. Fuzzy linguistic variables and fuzzy algorithms offer an effective, more flexible way to describe a system's behavior too complex for a classical mathematical model. They are very successful in economics, management science, artificial intelligence, information retrieval systems, pattern recognition, image processing, psychology, biology, and other fields rendered inherently fuzzy do to the unpredictable behavior of their components. Expert systems, fuzzy neural computing and pattern recognition are discussed in some detail.