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Fuzzy logic and fuzzy control

Fuzzy logic and fuzzy control have been a main research focus at this department since the mid-seventies. After 15 years of purely theoretical research, the FLLL (Fuzzy Logic Laboratorium Linz-Hagenberg) was founded in the Softwarepark Hagenberg, aiming at applying these technologies to solve industrial problems.

Fuzzy logic is a many-valued logic, replacing the two classical truth values true (= 1) and false (= 0) by a continuum of truth values, usually represented by the unit interval [0,1]. Fuzzy sets, based on this many-valued logic, can be used to model linguistic vagueness which is intrinsically hidden in attributes like “large” and “small” and, in particular, the gradual transition between them. A main application of fuzzy logic is human-like reasoning in situations where vague, incomplete and/or (partially) contradictory knowledge is available, often in the form of rule-based systems as in fuzzy control.

The theoretical work at the department is related to foundations of fuzzy logic and fuzzy control with a special emphasis on logical operations, in particular triangular norms (see also the monograph Triangular norms). A special feature is the Linz Seminar on Fuzzy Set Theory, organized annually since 1979.

Practical applications of fuzzy logic and fuzzy control include industrial processes, image and signal processing, fault detection and knowledge-based modelling.