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This unique compendium represents important action of fuzzy systems to quantum mechanics. From fuzzy sets to fuzzy systems, it also gives clear descriptions on the development on fuzzy logic, where the most important result is the probability presentation of fuzzy systems.The important conclusions on fuzzy systems are used in the study of quantum mechanics, which is a very new idea. Eight important conclusions are obtained. The author has proved that mass-point motions in classical mechanics must have waves, which means that any mass-point motion in classical mechanics has wave mass-point dualism as well as any microscopic particle motion must have wave-particle dualism. Based on this conclusion, it has been proven that classical mechanics and quantum mechanics are unified.

This book systematically synthesizes research achievements in the field of fuzzy neural networks in recent years. It also provides a comprehensive presentation of the developments in fuzzy neural networks, with regard to theory as well as their application to system modeling and image restoration. Special emphasis is placed on the fundamental concepts and architecture analysis of fuzzy neural networks. The book is unique in treating all kinds of fuzzy neural networks and their learning algorithms and universal approximations, and employing simulation examples which are carefully designed to help the reader grasp the underlying theory. This is a valuable reference for scientists and engineers working in mathematics, computer science, control or other fields related to information processing. It can also be used as a textbook for graduate courses in applied mathematics, computer science, automatic control and electrical engineering.