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**Introduction to neuro-fuzzy systems.**
*(English)*
Zbl 0937.68098

Advances in Soft Computing. Heidelberg: Physica-Verlag. xii, 289 p. (2000).

The book explains the mathematical background of fuzzy systems, artificial neural networks, and fuzzy neural networks as combinations thereof. Chapter 1 introduces the basics of fuzzy set theory needed to understand linguistic variables and inference mechanisms. Next, the author introduces approximate reasoning and fuzzy logic controllers. Artificial Neural Networks (NNs) are discussed in Chapter 2. The emphasis is on learning rules. The perceptron learning, delta and generalized delta learning (backpropagation), and the winner-take-all (competitive learning) are detailed. Chapter 3 presents fuzzy neural networks. First, models of fuzzy neurons are defined. Fuzzy NNs are regarded as fuzzified artificial NNs and are grouped into seven types: from Type 1, where weights and targets are crisp and the inputs are fuzzy to Type 7, where weights and inputs are fuzzy and targets are crisp. The author proceeds to discuss hybrid NNs and the training of some of the fuzzy NN types. Training of neuro-fuzzy controllers and classifiers is also shown in brief. Each chapter concludes with a list of applications (from industry, management, financial markets, etc.) and extensive bibliography. A case study and a series of exercises, accompanied by solutions, are given in the Appendix. The numerous illustrations and examples, coupled with the apt mathematical detail make the book suitable as a course text and also a good reference source.

Reviewer: Ludmila Kuncheva (Bangor)

### MSC:

68T05 | Learning and adaptive systems in artificial intelligence |

68-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science |