Studies in Fuzziness and Soft Computing

By: Andrzej Piegat

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Hardcover | 8 May 2001

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748 Pages

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23.5 x 15.88 x 4.45

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In the last ten years, a true explosion of investigations into fuzzy modeling and its applications in control, diagnostics, decision making, optimization, pattern recognition, robotics, etc. has been observed. The attraction of fuzzy modeling results from its intelligibility and the high effectiveness of the models obtained. Owing to this the modeling can be applied for the solution of problems which could not be solved till now with any known conventional methods. The book provides the reader with an advanced introduction to the problems of fuzzy modeling and to one of its most important applications: fuzzy control. It is based on the latest and most significant knowledge of the subject and can be used not only by control specialists but also by specialists working in any field requiring plant modeling, process modeling, and systems modeling, e.g. economics, business, medicine, agriculture,and meteorology.

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Published: 6th November 2010

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Introduction	p. 1
Essence of fuzzy set theory	p. 1
Development of fuzzy set theory	p. 6
Basic Notions of Fuzzy Set Theory	p. 11
Fuzzy sets	p. 11
Characteristic parameters (indices) of a fuzzy set	p. 22
Linguistic modifiers of fuzzy sets	p. 27
Types of membership functions of fuzzy sets	p. 34
Type 2 fuzzy sets	p. 52
Fuzziness and probability: two kinds of uncertainty	p. 56
Arithmetic of Fuzzy Sets	p. 59
The extension principle	p. 60
Addition of fuzzy numbers	p. 67
Subtraction of fuzzy numbers	p. 75
Multiplication of fuzzy numbers	p. 79
Division of fuzzy numbers	p. 95
Peculiarities of fuzzy numbers	p. 100
Differences between fuzzy numbers and linguistic values	p. 107
Mathematics of Fuzzy Sets	p. 111
Basic operations on fuzzy sets	p. 111
Intersection operation (logical product) of fuzzy sets	p. 112
Union (logical sum) of fuzzy sets	p. 126
Compensatory operators	p. 132
Fuzzy relations	p. 136
Implication	p. 149
Fuzzy Models	p. 157
Structure, main elements and operations in fuzzy models	p. 157
Fuzzification	p. 159
Inference	p. 160
Defuzzification of the resulting membership function of the rule-base conclusion	p. 184
Example of fuzzy modeling	p. 199
Significant features of rules, rule bases and fuzzy models	p. 202
Local character of rules	p. 202
Dependence of the number of rules on the number of inputs and fuzzy sets	p. 204
Completeness of a fuzzy model	p. 208
Consistency of the rule base	p. 216
Continuity of the rule base	p. 219
Redundancy of the rule base	p. 222
Advice relating to rule base construction	p. 224
Reduction of the rule base	p. 229
Normalization (scaling) of the fuzzy model inputs and output	p. 244
Extrapolation in fuzzy models	p. 250
Types of fuzzy models	p. 280
Mamdani models	p. 281
Takagi-Sugeno models	p. 301
Relational models	p. 311
Global and local fuzzy models	p. 316
Fuzzy multimodels	p. 323
Neuro-fuzzy models	p. 329
Alternative models	p. 331
Similarity principles of the system and of the system model	p. 338
Fuzzy classification	p. 339
Methods of Fuzzy Modeling	p. 363
Fuzzy modeling based on the system expert's knowledge	p. 366
Creation of fuzzy, self-tuning models based on input/output measurement data of the system	p. 373
Application of neuro-fuzzy networks for fuzzy model parameter tuning	p. 374
Tuning of fuzzy model parameters with the genetic algorithm method	p. 400
Creation of self-organizing and self-tuning fuzzy models based on input/output measurement data of the system	p. 405
Determination of significant and insignificant inputs of the model	p. 406
Determining of fuzzy curves	p. 410
Self-organization and self-tuning tuning of fuzzy model parameters	p. 417
Fuzzy Control	p. 495
Static fuzzy controllers	p. 495
Dynamic fuzzy controllers	p. 500
The determination of structures and parameters for fuzzy controllers (organization and tuning)	p. 511
The design of fuzzy controllers on the basis of expert knowledge concerning plant under control	p. 512
The design of a fuzzy controller on the basis of a model of the expert controlling the plant	p. 516
The design of a fuzzy controller on the basis of the model of controlled plant	p. 522
The Stability of Fuzzy Control Systems	p. 609
The stability of fuzzy control systems with unknown models of plants	p. 614
The circle stability criterion	p. 618
The application of hyperstability theory to analysis of fuzzy-system stability	p. 625
The frequency domain representation of hyperstability conditions for control systems with a time invariant non-linear part	p. 627
The time domain conditions for hyperstability of continuous, non-linear control systems containing a time-invariant non-linear part	p. 655
The frequency domain conditions for hyperstability of discrete, non-linear control systems containing a time-invariant non-linear part	p. 657
References	p. 705
Index	p. 725
Table of Contents provided by Blackwell. All Rights Reserved.

Studies in Fuzziness and Soft Computing

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