This book contains introductory material to neuro-fuzzy systems. Its main purpose is to explain the information processing in mostly-used fuzzy inference systems, neural networks and neuro-fuzzy systems. More than 180 figures and a large number of (numerical) exercises (with solutions) have been inserted to explain the principles of fuzzy, neural and neuro-fuzzy systems. Also the mathematics applied in the models is carefully explained, and in many cases exact computational formulas have been derived for the rules in error correction learning procedures. Numerous models treated in the book will help the reader to design his own neuro-fuzzy system for his specific (managerial, industrial, financial) problem. The book can serve as a textbook for students in computer and management sciences who are interested in adaptive technologies.

Fuzzy and Neuro-Fuzzy Systems in Medicineprovides a thorough review of state-of-the-art techniques and practices, defines and explains relevant problems, as well as provides solutions to these problems. After an introduction, the book progresses from one topic to another - with a linear development from fundamentals to applications.

Neural Fuzzy Systems provides a comprehensive, up-to-date introduction to the basic theories of fuzzy systems and neural networks, as well as an exploration of how these two fields can be integrated to create Neural-Fuzzy Systems. It includes Matlab software, with a Neural Network Toolkit, and a Fuzzy System Toolkit.

Foundations of Neuro-Fuzzy Systems reflects the current trend in intelligent systems research towards the integration of neural networks and fuzzy technology. The authors demonstrate how a combination of both techniques enhances the performance of control, decision-making and data analysis systems. Smarter and more applicable structures result from marrying the learning capability of the neural network with the transparency and interpretability of the rule-based fuzzy system. Foundations of Neuro-Fuzzy Systems highlights the advantages of integration making it a valuable resource for graduate students and researchers in control engineering, computer science and applied mathematics. The authors' informed analysis of practical neuro-fuzzy applications will be an asset to industrial practitioners using fuzzy technology and neural networks for control systems, data analysis and optimization tasks.

Fuzzy sets were introduced by Zadeh (1965) as a means of representing and manipulating data that was not precise, but rather fuzzy. Fuzzy logic pro vides an inference morphology that enables approximate human reasoning capabilities to be applied to knowledge-based systems. The theory of fuzzy logic provides a mathematical strength to capture the uncertainties associ ated with human cognitive processes, such as thinking and reasoning. The conventional approaches to knowledge representation lack the means for rep resentating the meaning of fuzzy concepts. As a consequence, the approaches based on first order logic and classical probablity theory do not provide an appropriate conceptual framework for dealing with the representation of com monsense knowledge, since such knowledge is by its nature both lexically imprecise and noncategorical. The developement of fuzzy logic was motivated in large measure by the need for a conceptual framework which can address the issue of uncertainty and lexical imprecision. Some of the essential characteristics of fuzzy logic relate to the following [242]. • In fuzzy logic, exact reasoning is viewed as a limiting case of ap proximate reasoning. • In fuzzy logic, everything is a matter of degree. • In fuzzy logic, knowledge is interpreted a collection of elastic or, equivalently, fuzzy constraint on a collection of variables. • Inference is viewed as a process of propagation of elastic con straints. • Any logical system can be fuzzified. There are two main characteristics of fuzzy systems that give them better performance für specific applications.

A general neural-network-based connectionist model, called Fuzzy Neural Network (FNN), is proposed in this book for the realization of a fuzzy logic control and decision system. The FNN is a feedforward multi-layered network which integrates the basic elements and functions of a traditional fuzzy logic controller into a connectionist structure which has distributed learning abilities.In order to set up this proposed FNN, the author recommends two complementary structure/parameter learning algorithms: a two-phase hybrid learning algorithm and an on-line supervised structure/parameter learning algorithm.Both of these learning algorithms require exact supervised training data for learning. In some real-time applications, exact training data may be expensive or even impossible to get. To solve this reinforcement learning problem for real-world applications, a Reinforcement Fuzzy Neural Network (RFNN) is further proposed. Computer simulation examples are presented to illustrate the performance and applicability of the proposed FNN, RFNN and their associated learning algorithms for various applications.

Gain insight into fuzzy logic and neural networks, and how the integration between the two models makes intelligent systems in the current world. This book simplifies the implementation of fuzzy logic and neural network concepts using Python. You’ll start by walking through the basics of fuzzy sets and relations, and how each member of the set has its own membership function values. You’ll also look at different architectures and models that have been developed, and how rules and reasoning have been defined to make the architectures possible. The book then provides a closer look at neural networks and related architectures, focusing on the various issues neural networks may encounter during training, and how different optimization methods can help you resolve them. In the last section of the book you’ll examine the integrations of fuzzy logics and neural networks, the adaptive neuro fuzzy Inference systems, and various approximations related to the same. You’ll review different types of deep neuro fuzzy classifiers, fuzzy neurons, and the adaptive learning capability of the neural networks. The book concludes by reviewing advanced neuro fuzzy models and applications. What You’ll Learn Understand fuzzy logic, membership functions, fuzzy relations, and fuzzy inferenceReview neural networks, back propagation, and optimizationWork with different architectures such as Takagi-Sugeno model, Hybrid model, genetic algorithms, and approximations Apply Python implementations of deep neuro fuzzy system Who This book Is For Data scientists and software engineers with a basic understanding of Machine Learning who want to expand into the hybrid applications of deep learning and fuzzy logic.

Flexible Neuro-Fuzzy Systems is the first professional literature about the new class of powerful, flexible fuzzy systems. The author incorporates various flexibility parameters to the construction of neuro-fuzzy systems. This approach dramatically improves their performance, allowing the systems to perfectly represent the pattern encoded in data. Flexible Neuro-Fuzzy Systems is the only book that proposes a flexible approach to fuzzy modeling and fills the gap in existing literature. This book introduces new fuzzy systems which outperform previous approaches to system modeling and classification, and has the following features: -Provides a framework for unification, construction and development of neuro-fuzzy systems; -Presents complete algorithms in a systematic and structured fashion, facilitating understanding and implementation, -Covers not only advanced topics but also fundamentals of fuzzy sets, -Includes problems and exercises following each chapter, -Illustrates the results on a wide variety of simulations, -Provides tools for possible applications in business and economics, medicine and bioengineering, automatic control, robotics and civil engineering.

The second edition of this textbook provides a fully updated approach to fuzzy sets and systems that can model uncertainty — i.e., “type-2” fuzzy sets and systems. The author demonstrates how to overcome the limitations of classical fuzzy sets and systems, enabling a wide range of applications from time-series forecasting to knowledge mining to control. In this new edition, a bottom-up approach is presented that begins by introducing classical (type-1) fuzzy sets and systems, and then explains how they can be modified to handle uncertainty. The author covers fuzzy rule-based systems – from type-1 to interval type-2 to general type-2 – in one volume. For hands-on experience, the book provides information on accessing MatLab and Java software to complement the content. The book features a full suite of classroom material.

The second edition of this book provides a comprehensive introduction to a consortium of technologies underlying soft computing, an evolving branch of computational intelligence, which in recent years, has turned synonymous to it. The constituent technologies discussed comprise neural network (NN), fuzzy system (FS), evolutionary algorithm (EA), and a number of hybrid systems, which include classes such as neuro-fuzzy, evolutionary-fuzzy, and neuro-evolutionary systems. The hybridization of the technologies is demonstrated on architectures such as fuzzy backpropagation network (NN-FS hybrid), genetic algorithm-based backpropagation network (NN-EA hybrid), simplified fuzzy ARTMAP (NN-FS hybrid), fuzzy associative memory (NN-FS hybrid), fuzzy logic controlled genetic algorithm (EA-FS hybrid) and evolutionary extreme learning machine (NN-EA hybrid) Every architecture has been discussed in detail through illustrative examples and applications. The algorithms have been presented in pseudo-code with a step-by-step illustration of the same in problems. The applications, demonstrative of the potential of the architectures, have been chosen from diverse disciplines of science and engineering. This book, with a wealth of information that is clearly presented and illustrated by many examples and applications, is designed for use as a text for the courses in soft computing at both the senior undergraduate and first-year postgraduate levels of computer science and engineering. It should also be of interest to researchers and technologists desirous of applying soft computing technologies to their respective fields of work.