Uncertain rule-based fuzzy logic systems introdution and new directions

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Language: English
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560 p. · 19x23 cm · Hardback
For graduate-level courses in Neural Networks and Fuzzy Systems, Fuzzy Systems/Control, Fuzzy Logic.
The first book of its kind, this text explains how all kinds of uncertainties can be handled within the framework of a common theory and set of design tools fuzzy logic systems by moving the original fuzzy logic to the next level type-2 fuzzy logic. It presents a complete development of both type-1 and type-2 fuzzy logic systems, showing how the expanded and richer fuzzy logic contains the original fuzzy logic within it. The text demonstrates, beyond a reasonable doubt, that when uncertainties are present in a problem, much better performance is obtained by using a type-2 fuzzy logic system than by using a type-1 fuzzy logic system.
I. PRELIMINARIES.
1. Introduction.
2. Sources of Uncertainty.
3. Membership Functions and Uncertainty.
4. Case Studies.
II. TYPE-1 FUZZY LOGIC SYSTEMS.
5. Singleton Type-1 Fuzzy Logic Systems: No Uncertainties.
6. Non-singleton Type-1 Fuzzy Logic Systems.
III. TYPE-2 FUZZY SETS.
7. Operations on and Properties of Type-2 Fuzzy Sets.
8. Type-2 Relations and Compositions.
9. Centroid of a Type-2 Fuzzy Set: Type Reduction.
IV. TYPE-2 FUZZY LOGIC SYSTEMS.
10. Singleton Type-2 Fuzzy Logic Systems.
11. Type-1-Non-singleton Type-2 Fuzzy Logic Systems.
12. Type-2-Non-singleton Type-2 Fuzzy Logic Systems.
13. TSK Fuzzy Logic Systems.
14. Epilogue.
Appendix A: Join, Meet and Negation Operations for Non- interval Type-2 Fuzzy Sets.
Appendix B: Properties of Type-1 and Type-12 Fuzzy Sets.
Appendix C: Computation.
References.
  • A self-contained pedagogical approach - Not a handbook.
  • An expanded rule-based fuzzy logic - Type-2 fuzzy logic-is able to handle uncertainties because it can model them and minimize their effects, and, if all uncertainties disappear, type-2 fuzzy logic reduces to type-1 fuzzy logic, in much the same way that if randomness disappears, then probability reduces to determinism - shows students how to use fuzzy logic in new ways and how to effectively solve problems that are awash in uncertainties.
  • A bottom-up approach - Begins with type-1 fuzzy logic systems and explains how they are modified to the simplest kind of type-2 fuzzy logic system, then add layers of complexity to that system.
  • Two short primers on fuzzy sets and fuzzy logic - Amply illustrated with examples