## Uncertain Rule-based Fuzzy Logic Systems: Introduction and New DirectionsPreface Uncertainty is the fabric that makes life interesting. For millenia human beings have developed strategies to cope with a plethora of uncertainties, never absolutely sure what the consequences would be, but hopeful that the deleterious effects of those uncertainties could be minimized. This book presents a complete methodology for accomplishing this within the framework of fuzzy logic (FL). This is not the original FL, but is an expanded and richer FL, one that contains the original FL within it. The original FL, founded by Lotfi Zadeh, has been around for more than 35 years, as of the year 2000, and yet it is unable to handle uncertainties. By Although many applications were found for type-1 FL, it is its application to FL has already been applied in numerous fields, in many of which uncertainties are present (e.g., signal processing, digital communications, computer and communication networks, diagnostic medicine, operations research, financial investing, control, etc.). Hence, the results in this book can immediately be used in all of these fields. To demonstrate the performance advantages for type-2 FLSs over their type-1 counterparts, when uncertainties are present, I describe and provide results for the following applications in this book: forecasting of time series, knowledge-mining using surveys, classification of video data working directly with compressed data, equalization of time-varying nonlinear digital communication channels, overcoming co-channel interference and intersymbol interference for time-varying nonlinear digital communication channels, and connection admission control for asynchronous transfer mode networks. No control applications have been included, because to date type-2 FL has not yet been applied to them; hence, this book is not about FL control, although its methodologies may someday be applicable to it. I have organized this book into four parts. Part 1— This book can be read by anyone who has an undergraduate BS degree and should be of great interest to computer scientists and engineers who already use or want to use rule-based systems and are concerned with how to handle uncertainties about such systems. I have included many worked-out examples in the text, and have also included homework problems at the end of most chapters so that the book can be used in a classroom setting as well as a technical reference. Here are some specific ways that this book can be used: - For the person totally unfamiliar with FL who wants a quick introduction to it, read the Supplement to Chapter 1 and Chapter 5 (Sections 5.1-5.8).
- For the person who wants an in-depth treatment of type-1 rule-based FLSs, read the Supplement to Chapter 1 and Chapters 4-6.
- For the person who is only interested in type-2 fuzzy set theory, read Chapters 3, 7-9, and Appendices A and B.
- For a person who wants to give a course on rule-based fuzzy logic systems, use Chapters 1-12 and 13 (if time permits). Chapter 14 should be of interest to people with a background in digital communications, pattern recognition, or communication networks and will suggest projects for a course.
- For a person who is a proponent of Takagi-Sugeno-Kang (TSK) fuzzy systems and wants to see what their type-2 counterparts look like, read Chapters 3, 7-9, and 13.
- For a person who is interested in forecasting of time-series and wants to get a quick overview of the benefits to modeling uncertainties on forecasting performance when using rule-based forecasters, read Chapters 4 (Section 4.2), 5 (Section 5.10), 6 (Section 6.7), 10 (Section 10.11), 11 (Section 11.5), and 12 (Section 12.5).
- For a person who is interested in knowledge mining and wants to get a quick overview of the benefits to modeling uncertainties on judgment making when using rule-based advisors, read Chapters 4 (Section 4.3), 5 (Section 5.11), and 10 (Section 10.12).
So that people will start using type-2 FL as soon as possible, I have made free software available online for implementing and designing type-1 and type-2 FLSs. It is MATLAB-based (MATLAB is a registered trademark of The MathWorks, Inc.), was developed by my former PhD students Nilesh Karnik and Qilian Liang, and can be reached at:http://sipi.usc.edu/. A computation section, which directs the reader to very specific M-files, appears at the end of most chapters of this book. Appendix C summarizes all of the M-files so that the reader can see the forest from the trees. |

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### Contents

Singleton Type2 Fuzzy Logic | 17 |

short primers on fuzzy sets | 19 |

Sources of Uncertainty | 66 |

Copyright | |

14 other sections not shown

### Common terms and phrases

### References to this book

Fuzzy Decision Making in Modeling and Control Joćo M. C. Sousa,Uzay Kaymak No preview available - 2002 |