Logic based on the concept of fuzzy sets, in which membership is expressed in varying probabilities or degrees of truth—that is, as a continuum of values ranging from 0 (does not occur) to 1 (definitely occurs). As additional data are gathered, many fuzzy-logic systems are able to adjust the probability values assigned to different parameters. Because some such systems appear able to learn from their mistakes, they are often considered a crude form of artificial intelligence. The term and concept date from a 1965 paper by Lotfi A. Zadeh (born 1921). Fuzzy-logic systems achieved commercial application in the early 1990s. Advanced clothes-washing machines, for example, use fuzzy-logic systems to detect and adapt to patterns of water movement during a wash cycle, increasing efficiency and reducing water consumption. Other products using fuzzy logic include camcorders, microwave ovens, and dishwashers. Other applications include expert systems, self-regulating industrial controls, and computerized speech- and handwriting-recognition programs.
Learn more about fuzzy logic with a free trial on Britannica.com.
The strength of neuro-fuzzy systems involves two contradictory requirements in fuzzy modeling: interpretability versus accuracy. In practice, one of the two properties prevails. The neuro-fuzzy in fuzzy modeling research field is divided into two areas: linguistic fuzzy modeling that is focused on interpretability, mainly the Mamdani model; and precise fuzzy modeling that is focused on accuracy, mainly the Takagi-Sugeno-Kang (TSK) model.
It must be pointed out that interpretability of the Mamdani-type neuro-fuzzy systems can be lost. To improve the interpretability of neuro-fuzzy systems, certain measures must be taken, wherein important aspects of interpretability of neuro-fuzzy systems are also discussed.
Three members of POPFNN exist in the literature:
The "POPFNN" architecture is a five-layer neural network where the layers from 1 to 5 are called: input linguistic layer, condition layer, rule layer, consequent layer, output linguistic layer. The fuzzification of the inputs and the defuzzification of the outputs are respectively performed by the input linguistic and output linguistic layers while the fuzzy inference is collectively performed by the rule, condition and consequence layers.
The learning process of POPFNN consists of three phases:
Various fuzzy membership generation algorithms can be used: Learning Vector Quantization (LVQ), Fuzzy Kohonen Partitioning (FKP) or Discrete Incremental Clustering (DIC). Generally, the POP algorithm and its variant LazyPOP are used to identify the fuzzy rules.