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This book presents a systematic study on the inherent complexity in fuzzy systems, resulting from the large number and the poor transparency of the fuzzy rules. The study uses a novel approach for complexity management, aimed at compressing the fuzzy rule base by removing the redundancy while preserving the solution. The compression is based on formal methods for presentation, manipulation, transformation and simplification of fuzzy rule bases, which are illustrated by algorithms as well as results from numerous examples and two case studies. The results are directly applicable or easily extendable to a wide class of fuzzy systems and detailed benchmarks for expanding these systems to new areas such as fuzzy networks and fuzzy multi-agent systems are introduced. The intended readers are people from both academia and industry, who would be interested in building and implementing advanced fuzzy systems.