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Introduction to type-2 fuzzy logic control: theory and applications

Written by world-class leaders in type-2 fuzzy logic control, this book offers a self-contained reference for both researchers and students. The coverage provides both background and an extensive literature survey on fuzzy logic and related type-2 fuzzy control. It also includes research questions, experiment and simulation results, and downloadable computer programs on an associated website. This key resource will prove useful to students and engineers wanting to learn type-2 fuzzy control theory and its applications

Properties of a Fuzzy Relational Model

This report describes the properties of a fuzzy relational model and a simple identification algorithm based on fuzzy matching. It is shown that a one-input one-output fuzzy model, with triangular membership functions, is able to exactly model a continuous piecewise linear system. Next, a characteristic of the fuzzy identification technique which reduces the size of the relational model, and hence the memory requirement is presented. The data distribution needed to exactly identify a linear system is also established, and this result leads to the derivation of an error equation. 1 Introduction Increasingly, artificial intelligence techniques, such as fuzzy logic and neural networks, are employed in model-based control strategies. This shift towards fuzzy models and neural networks has been fueled in part by the realisation that they can approximate a continuous non-linear function to an arbitrary accuracy (Kosko, 1994). However, it is unclear what form the model should take in order t..

Introduction to Type-2 Fuzzy Logic Control

When Lotfi Zadeh invented fuzzy sets in 1965, he never dreamt that the field in which they would be most widely used would arguably be the one that became the most hostile to the concept of fuzziness, namely control. Perhaps this was because the word "fuzzy" in Western civilization does not have a positive connotation and suggests an abandonment of mathematical rigor, one of the cornerstones of control. Perhaps it was because some famous mathematical probabilists (incorrectly) claimed that there was no difference between a fuzzy set and subjective probability. Perhaps it was because for almost a decade, until the 1974 seminal paper by Prof. Ebrahim Mamdani, who founded the field of fuzzy logic control and to whose memory our book is dedicated, there were no substantial real-world applications for fuzzy sets. Or, perhaps, it was because after the founding of this field many exaggerated claims were made by the fuzzy logic control community that flew in the face of mathematical rigor and did not pay attention to the same metrics that were and still are the cornerstones for control and cannot be ignored