The importance of Trustworthy and Explainable Artificial Intelligence (XAI) is recognized in academia, industry and society. This book introduces tools for dealing with imprecision and uncertainty in XAI applications where explanations are demanded, mainly in natural language. Design of Explainable Fuzzy Systems (EXFS) is rooted in Interpretable Fuzzy Systems, which are thoroughly covered in the book. The idea of interpretability in fuzzy systems, which is grounded on mathematical constraints and assessment functions, is firstly introduced. Then, design methodologies are described. Finally, the book shows with practical examples how to design EXFS from interpretable fuzzy systems and natural language generation. This approach is supported by open source software. The book is intended for researchers, students and practitioners who wish to explore EXFS from theoretical and practical viewpoints. The breadth of coverage will inspire novel applications and scientific advancements.

Written by one of the foremost experts in the field of neural networks, this is the first book to combine the theories and applications or neural networks and fuzzy systems. The book is divided into three sections: Neural Network Theory, Neural Network Applications, and Fuzzy Theory and Applications. It describes how neural networks can be used in applications such as: signal and image processing, function estimation, robotics and control, analog VLSI and optical hardware design; and concludes with a presentation of the new geometric theory of fuzzy sets, systems, and associative memories.

This book is devoted to reporting innovative and significant progress in fuzzy system engineering. Given the maturation of fuzzy logic, this book is dedicated to exploring the recent breakthroughs in fuzziness and soft computing in favour of intelligent system engineering. This monograph presents novel developments of the fuzzy theory as well as interesting applications of the fuzzy logic exploiting the theory to engineer intelligent systems.

This book presents a variety of recently developed methods for generating fuzzy rules from data with the help of neural networks and evolutionary algorithms. Special efforts have been put on dealing with knowledge incorporation into neural and evolutionary systems and knowledge extraction from data with the help of fuzzy logic. On the one hand, knowledge that is understandable to human beings can be extracted from data using evolutionary and learning methods by maintaining the interpretability of the generated fuzzy rules. On the other hand, a priori knowledge like expert knowledge and human preferences can be incorporated into evolution and learning, taking advantage of the knowledge representation capability of fuzzy rule systems and fuzzy preference models. Several engineering application examples in the fields of intelligent vehicle systems, process modeling and control and robotics are presented.

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.

In today’s real-world applications, there is an increasing demand of integrating new information and knowledge on-demand into model building processes to account for changing system dynamics, new operating conditions, varying human behaviors or environmental influences. Evolving fuzzy systems (EFS) are a powerful tool to cope with this requirement, as they are able to automatically adapt parameters, expand their structure and extend their memory on-the-fly, allowing on-line/real-time modeling. This book comprises several evolving fuzzy systems approaches which have emerged during the last decade and highlights the most important incremental learning methods used. The second part is dedicated to advanced concepts for increasing performance, robustness, process-safety and reliability, for enhancing user-friendliness and enlarging the field of applicability of EFS and for improving the interpretability and understandability of the evolved models. The third part underlines the usefulness and necessity of evolving fuzzy systems in several online real-world application scenarios, provides an outline of potential future applications and raises open problems and new challenges for the next generation evolving systems, including human-inspired evolving machines. The book includes basic principles, concepts, algorithms and theoretic results underlined by illustrations. It is dedicated to researchers from the field of fuzzy systems, machine learning, data mining and system identification as well as engineers and technicians who apply data-driven modeling techniques in real-world systems.

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.

Introduction to Fuzzy Systems provides students with a self-contained introduction that requires no preliminary knowledge of fuzzy mathematics and fuzzy control systems theory. Simplified and readily accessible, it encourages both classroom and self-directed learners to build a solid foundation in fuzzy systems. After introducing the subjec

Intelligence systems. We perfonn routine tasks on a daily basis, as for example: • recognition of faces of persons (also faces not seen for many years), • identification of dangerous situations during car driving, • deciding to buy or sell stock, • reading hand-written symbols, • discriminating between vines made from Sauvignon Blanc, Syrah or Merlot grapes, and others. Human experts carry out the following: • diagnosing diseases, • localizing faults in electronic circuits, • optimal moves in chess games. 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 ifthey 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 perfonn tasks difficult or impossible to do for humans, as for example: compression of signals and digital channel equalization.

Traces the story of Lofti Zadeh, an Iranian-American professor at Berkeley who began developing fuzzy logic - the way to program computers so they can mimic the imprecise way that humans make decisions.