Czogała E., Łęski J. Fuzzy and Neuro-Fuzzy Intelligent Systems

Physica-Verlag, 2000. — 207.It is possible to design artificial systems to replace or "duplicate" the human expert. There are many possible definitions of intelligence systems. One of them is that: an intelligence system is a system able to make decisions that would be regarded as intelligent if they were observed in humans. Intelligence systems adapt themselves using some example situations (inputs of a system) and their correct decisions (system's output). The system after this learning phase can make decisions automatically for future situations. This system can also perform tasks difficult or impossible to do for humans, as for example: compression of signals and digital channel equalization.
Artificial neural networks. Since humans can perform many tasks presented at the beginning of this preface better than the best machines, human brain has been of great interest for engineers. This led to perceptron in the late 50s and to artificial neural networks (ANNs) in mid 80s. ANNs were originally developed with a view to modeling learning and processing information in the brain. For the purpose of this book, the ANNs is an important tool in the arsenal of machine-learning techniques, rather than model of the brain. Prof. S. Haykin proposed the following definition of ANNs: "A neural network is a massively parallel distributed processor made up of simple processing units, which has a natural propensity for storing experiential knowledge and making it available for use. It resembles the brain in two respects: knowledge is acquired by the network from its environment through a learning process, interneuron connection strengths, known as synaptic weights, are used to store the acquired knowledge." In practice the majority of ANNs works on single-processor computers.
The most common mode of learning for both humans and ANNs is supervised. In this case we have some situations (examples) and correct decisions, which formulate a training set. If we have only situations without correct decisions, then ANNs can perform unsupervised learning, which is often called clustering. In this mode ANNs search for structures of data. Both types of learning will be used in this book for the construction of neuro-fuzzy systems.
Neuro-fuzzy systems. In most fuzzy systems fuzzy if-then rules were obtained from the human expert. However, this method of knowledge acquisition has great disadvantages: not every expert can and/or wants to share his knowledge. Artificial neural networks were incorporated into fuzzy systems forming the so-called neuro-fuzzy systems, which can acquire knowledge automatically by learning algorithms of neural networks. The neuro-fuzzy systems have advantages over fuzzy systems, i.e. acquired knowledge is easy to understand (are more meaningful) to humans. Like in neural networks knowledge is saved in connection weights, but can be easily interpreted as fuzzy if-then rules.
The most frequently used neural networks in neuro-fuzzy systems are radial basis function networks. Their popularity is due to the simplicity of structure, well-established theoretical basis and faster learning than in other types of artificial neural networks.
If the number of input variables is large then it is very difficult to apply neuro-fuzzy systems, because the input space is divided into a very large number of fuzzy regions in which one if-then rule operates dominantly (Bellman's course of dimensionality). The neuro-fuzzy system can be viewed as a mixture oflocal experts (rules operate dominantly in each region). To determine these regions clustering method (unsupervised networks) for input or input-output space is often used. Clustering has been employed for initialization of unknown values of neuro-fuzzy system parameters such as: a number of fuzzy if-then rules and membership function of linguistic terms from premise parts of these rules. In the next step these parameters are updated using gradient and least squares optimization methods. Recently global optimization methods are frequently used to update neuro-fuzzy system parameters. Connection of fuzzy systems, artificial neural networks, clustering and optimization methods is usually called soft computing systems.Classical sets and fuzzy sets Basic definitions and terminology
Approximate reasoning
Artificial neural networks
Unsupervised learning Clustering methods
Fuzzy systems
Neuro-fuzzy systems
Applications of artificial neural network based fuzzy inference system