Fuzzy Neural Intelligent Systems: Mathematical Foundation and the Applications in EngineeringAlthough fuzzy systems and neural networks are central to the field of soft computing, most research work has focused on the development of the theories, algorithms, and designs of systems for specific applications. There has been little theoretical support for fuzzy neural systems, especially their mathematical foundations. Suitable for self-study, as a reference, and ideal as a textbook, Fuzzy Neural Intelligent Systems is accessible to students with a basic background in linear algebra and engineering mathematics. Mastering the material in this textbook will prepare students to better understand, design, and implement fuzzy neural systems, develop new applications, and further advance the field. |
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... functions , fuzzy sets can also be described by membership functions . If the range of μA admits only two values 0 and 1 , then μA degenerates into a usual set characteristic function . A = { uЄU | μA ( u ) = 1 } . Therefore , Cantor ...
... membership function of a complement fuzzy set Example 4 Let the fuzzy sets young ( Y ) and old ( O ) be defined as in Example 1. Then the fuzzy sets " young or old " ( YUO ) , " young and old " ( YnO ) , and " not young " ( Y ) are ...
... membership function is defined by : V ( u , v ) Є U × V , μA × B ( u , v ) = μA ( U ) ^ μB ( V ) . This is called the direct product ( or Cartesian product ) of A and B. 1.3 The Resolution Theorem In an actual application , people often ...
... membership function μxa ( u ) = \ ^ μA ( u ) , u ○ U . The new fuzzy set XA defined in this way is called the scalar product of A. It is easy to show that the following properties hold for the scalar product of fuzzy sets . 1 ) λ1 ≤ 2 ...
... Membership Functions In real world application of fuzzy sets , an important task is to determine mem- bership functions of the fuzzy sets in question . Like the estimation of probabilities in the probability theory , we can only obtain ...
Contents
1 | |
23 | |
Mathematical Essence and Structures of Feedforward Artificial Neural Networks | 47 |
Functionallink Neural Networks and Visualization Means of Some Mathematical Methods | 72 |
Flat Neural Networks and Rapid Learning Algorithms | 90 |
Basic Structure of Fuzzy Neural Networks | 113 |
Mathematical Essence and Structures of Feedback Neural Networks and Weight Matrix Design | 126 |
Generalized Additive Weighted Multifactorial Function and its Applications to Fuzzy Inference and Neural Networks | 140 |
Adaptive Fuzzy Controllers Based on Variable Universes | 181 |
The Basics of Factor Spaces | 197 |
Neuron Models Based on Factor Spaces Theory and Factor Space Canes | 219 |
Foundation of NeuroFuzzy Systems and an Engineering Application | 241 |
Data Preprocessing | 255 |
Control of a Flexible Robot Arm using a Simplified Fuzzy Controller | 267 |
Application of NeuroFuzzy Systems Development of a Fuzzy Learning Decision Tree and Application to Tactile Recognition | 295 |
Fuzzy Assessment Systems of Rehabilitative Process for CVA Patients | 322 |
The Interpolation Mechanism of Fuzzy Control | 152 |
The Relationship between Fuzzy Controllers and PID Controllers | 165 |
A DSPbased Neural Controller for a Multidegree Prosthetic Hand | 351 |
Other editions - View all
Fuzzy Neural Intelligent Systems: Mathematical Foundation and the ... Hongxing Li,C.L. Philip Chen,Han-Pang Huang No preview available - 2000 |