ABSTRACT
This chapter introduces the neuro-fuzzy system, as a combination of fuzzy system and neural networks and discusses with classic fuzzy systems, based on a simple case. The adaptive systems are best handled with methods of computational intelligence such as neural networks and fuzzy systems. Both of them consist of three blocks: fuzzification, fuzzy rules, and defuzzification/normalization. Fuzzification is supposed to convert the analog inputs into sets of fuzzy variables. Fuzzy variables are processed by fuzzy logic rules, with MIN and MAX operators. In the Takagi–Sugeno–Kang fuzzy systems, the defuzzification block was replaced with normalization and weighted average; MAX operations are not required, instead, a weighted average is applied directly to regions selected by MIN operators. The neuro-fuzzy system consists of four blocks: fuzzification, multiplication, summation, and division. A single neuron can divide input space by line, plane, or hyper plane, depending on the problem dimensionality.
