System identification is the task of constructing representative models of processes and has become an invaluable tool in many different areas of science and engineering. Due to the inherent complexity of many real world systems the application of traditional techniques is limited. In such instances more sophisticated (so called intelligent) modelling approaches are required. Neurofuzzy modelling is one such technique, which by integrating the attributes of fuzzy systems and neural networks is ideally suited to system identification. This attractive paradigm combines the well established learning techniques of a particular form of neural network i.e. generalised linear models with the transparent knowledge representation of fuzzy systems, thus producing models which possess the ability to learn from real world observations and whose behaviour can be described naturally as a series of linguistic humanly understandable rules. Unfortunately, the application of these systems is limited to low dimensional problems for which good quality expert knowledge and data are available. The work described in this thesis addresses this fundamental problem with neurofuzzy modelling, as a result algorithms which are less sensitive to the quality of the a priori knowledge and empirical data are developed. The true modelling capabilities of any strategy is heavily reliant on the model's structure, and hence an important (arguably the most important) task is structure identification. Also, due to the curse of dimensionality, in high dimensional problems the size of conventional neurofuzzy models gets prohibitively large. These issues are tackled by the development of automatic neurofuzzy model identification algorithms, which exploit the available expert knowledge and empirical data. To alleviate problems associated with the curse of dimensionality, aid model generalisation and enhance model transparency, parsimonious models are identified. This is achieved by the application of additive and multiplicative neurofuzzy models which exploit structural redundancies found in conventional systems. The developed construction algorithms successfully identify parsimonious models, but as a result of noisy and poorly distributed empirical data, these models can still generalise inadequately. This problem is addressed by the application of Bayesian inferencing techniques; a form of regularisation. Smooth model outputs are assumed and superfluous model parameters are controlled, sufficiently aiding model generalisation and transparency, and data interpolation and extrapolation. By exploiting the structural decomposition of the identified neurofuzzy models, an efficient local method of regularisation is developed. All the methods introduced in this thesis are illustrated on many different examples, including simulated time series, complex functional equations, and multi-dimensional dynamical systems. For many of these problems conventional neurofuzzy modelling is unsuitable, and the developed techniques have extended the range of problems to which neurofuzzy modelling can successfully be applied.

Conventional control systems express control solutions by means of expressions, usually mathematically based. In order to completely express the control solution, a vast amount of data is required. In contrast, knowledge-based solutions require far less plant data and mathematical expression. This reduces development time proportionally. In addition, because this type of processing does not require involved calculations, processing speed is increased, since rule process is separate and all processes can be performed simultaneously. These results in improved product quality, better plant efficiency, simplified process, etc. Within this project, conventional PID control has already been implemented, with the control parameter adjustment and loop tuning being problematic. This is mainly due to a number of external parameters that affects the stability of the process. In maintaining a consistent temperature, for example, the steam flow rate varies, the hot well temperature varies, the ambient may temperature vary. Another contributing factor, the time delay, also affects the optimization of the system, due to the fact that temperature measurement is based on principle of absorption. The normal practice in industry to avoid an unstable control condition is to have an experienced operator to switch the controller to manual, and make adjustments. After obtaining the desired PV, the controller is switched back to automatic. This research project focuses on eliminating this time loss, by implementing a knowledge-based controller, for intelligent decision-making. A FLC design tool, which allows full interaction, whilst designing the control algorithm, was used to optimize the control system. The design tool executed on a PC is connected to a PLC, which in turn is successfully integrated into the process plant.

In this thesis we first extend the notion of fuzzy normality to the notion of normality of a fuzzy subgroup in another fuzzy group. This leads to the study of normal series of fuzzy subgroups, and this study includes solvable and nilpotent fuzzy groups, and the fuzzy version of the Jordan-Hõlder Theorem. Furthermore we use the notion of normality to study products and direct products of fuzzy subgroups. We present a notion of fuzzy isomorphism which enables us to state and prove the three well-known isomorphism theorems and the fact that the internal direct product of two normal fuzzy subgroups is isomorphic to the external direct product of the same fuzzy subgroups. A brief discussion on fuzzy subgroups generated by fuzzy subsets is also presented, and this leads to the fuzzy version of the Basis Theorem. Finally, the notion of direct product enables us to study decomposable and indecomposable fuzzy subgroups, and this study includes the fuzzy version of the Remak-Krull-Schmidt Theorem.

published_or_final_version / Industrial and Manufacturing Systems Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Industrial and Manufacturing Systems Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

by Yeung Wai Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 92-[96]). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Fuzzy Inference and Real Intelligent Mapping --- p.1 / Chapter 1.2 --- Organization of the thesis --- p.5 / Chapter 2 --- Fuzzy Logic inference --- p.7 / Chapter 2.1 --- Fuzzy logic --- p.7 / Chapter 2.1.1 --- Fuzzy sets --- p.7 / Chapter 2.1.2 --- Operations on fuzzy sets --- p.10 / Chapter 2.2 --- Fuzzy Inference --- p.11 / Chapter 3 --- Weaknesses of fuzzy inference --- p.17 / Chapter 3.1 --- Is the use of linguistic fuzzy if-then rules and membership func- tions a good means of representing human expert knowledge? --- p.17 / Chapter 3.2 --- Role of conventional fuzzy inference doubtful if the expert knowl- edge is in the form of sampled input-output data --- p.21 / Chapter 3.3 --- Computational requirements --- p.23 / Chapter 3.4 --- Low transparency --- p.24 / Chapter 3.5 --- Analytical difficulties --- p.25 / Chapter 4 --- Real Intelligent Mapping --- p.27 / Chapter 5 --- Design of Real Intelligent Mapping Systems Using Dirichlet Tessellation --- p.33 / Chapter 5.1 --- Dirichlet tessellation for function approximation --- p.34 / Chapter 5.2 --- Identification of a DT based RIM system by least-squares --- p.42 / Chapter 5.3 --- Examples --- p.48 / Chapter 5.3.1 --- Defining the problem --- p.48 / Chapter 5.3.2 --- Balancing an inverted pendulum --- p.49 / Chapter 5.3.3 --- Balancing an inverted pendulum with cart --- p.53 / Chapter 5.3.4 --- Truck backing-up --- p.56 / Chapter 5.3.5 --- Chaotic time series prediction --- p.60 / Chapter 5.4 --- Interactive CAD platform for RIM systems design --- p.63 / Chapter 6 --- Analysis of Dirichlet tessellation based Real Intelligent Mapping Systems --- p.67 / Chapter 6.1 --- Local Stability Analysis of DT Based RIM Systems --- p.69 / Chapter 6.1.1 --- Balancing an inverted pendulum --- p.71 / Chapter 6.1.2 --- Truck backing-up --- p.73 / Chapter 6.2 --- Global stability analysis of DT based RIM systems --- p.74 / Chapter 6.3 --- Design of a stable DT based RIM system --- p.79 / Chapter 6.4 --- A method for analyzing Second order DT based RIM systems --- p.82 / Chapter 6.5 --- Piecewise-polynomial real domain representation of a class of fuzzy controller and its stability --- p.85 / Chapter 7 --- Conclusion --- p.90 / Bibliography --- p.92

by Ong Kai Hin George. / Thesis (M.Sc.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves [102-104]).

by Chung, Fu Lai. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 166-174). / ACKNOWLEDGEMENT --- p.iii / ABSTRACT --- p.iv / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Integration of Fuzzy Systems and Neural Networks --- p.1 / Chapter 1.2 --- Objectives of the Research --- p.7 / Chapter 1.2.1 --- Fuzzification of Competitive Learning Algorithms --- p.7 / Chapter 1.2.2 --- Capacity Analysis of FAM and FRNS Models --- p.8 / Chapter 1.2.3 --- Structure and Parameter Identifications of FRNS --- p.9 / Chapter 1.3 --- Outline of the Thesis --- p.9 / Chapter 2. --- A Fuzzy System Primer --- p.11 / Chapter 2.1 --- Basic Concepts of Fuzzy Sets --- p.11 / Chapter 2.2 --- Fuzzy Set-Theoretic Operators --- p.15 / Chapter 2.3 --- "Linguistic Variable, Fuzzy Rule and Fuzzy Inference" --- p.19 / Chapter 2.4 --- Basic Structure of a Fuzzy System --- p.22 / Chapter 2.4.1 --- Fuzzifier --- p.22 / Chapter 2.4.2 --- Fuzzy Knowledge Base --- p.23 / Chapter 2.4.3 --- Fuzzy Inference Engine --- p.24 / Chapter 2.4.4 --- Defuzzifier --- p.28 / Chapter 2.5 --- Concluding Remarks --- p.29 / Chapter 3. --- Categories of Fuzzy Neural Systems --- p.30 / Chapter 3.1 --- Introduction --- p.30 / Chapter 3.2 --- Fuzzification of Neural Networks --- p.31 / Chapter 3.2.1 --- Fuzzy Membership Driven Models --- p.32 / Chapter 3.2.2 --- Fuzzy Operator Driven Models --- p.34 / Chapter 3.2.3 --- Fuzzy Arithmetic Driven Models --- p.35 / Chapter 3.3 --- Layered Network Implementation of Fuzzy Systems --- p.36 / Chapter 3.3.1 --- Mamdani's Fuzzy Systems --- p.36 / Chapter 3.3.2 --- Takagi and Sugeno's Fuzzy Systems --- p.37 / Chapter 3.3.3 --- Fuzzy Relation Based Fuzzy Systems --- p.38 / Chapter 3.4 --- Concluding Remarks --- p.40 / Chapter 4. --- Fuzzification of Competitive Learning Networks --- p.42 / Chapter 4.1 --- Introduction --- p.42 / Chapter 4.2 --- Crisp Competitive Learning --- p.44 / Chapter 4.2.1 --- Unsupervised Competitive Learning Algorithm --- p.46 / Chapter 4.2.2 --- Learning Vector Quantization Algorithm --- p.48 / Chapter 4.2.3 --- Frequency Sensitive Competitive Learning Algorithm --- p.50 / Chapter 4.3 --- Fuzzy Competitive Learning --- p.50 / Chapter 4.3.1 --- Unsupervised Fuzzy Competitive Learning Algorithm --- p.53 / Chapter 4.3.2 --- Fuzzy Learning Vector Quantization Algorithm --- p.54 / Chapter 4.3.3 --- Fuzzy Frequency Sensitive Competitive Learning Algorithm --- p.58 / Chapter 4.4 --- Stability of Fuzzy Competitive Learning --- p.58 / Chapter 4.5 --- Controlling the Fuzziness of Fuzzy Competitive Learning --- p.60 / Chapter 4.6 --- Interpretations of Fuzzy Competitive Learning Networks --- p.61 / Chapter 4.7 --- Simulation Results --- p.64 / Chapter 4.7.1 --- Performance of Fuzzy Competitive Learning Algorithms --- p.64 / Chapter 4.7.2 --- Performance of Monotonically Decreasing Fuzziness Control Scheme --- p.74 / Chapter 4.7.3 --- Interpretation of Trained Networks --- p.76 / Chapter 4.8 --- Concluding Remarks --- p.80 / Chapter 5. --- Capacity Analysis of Fuzzy Associative Memories --- p.82 / Chapter 5.1 --- Introduction --- p.82 / Chapter 5.2 --- Fuzzy Associative Memories (FAMs) --- p.83 / Chapter 5.3 --- Storing Multiple Rules in FAMs --- p.87 / Chapter 5.4 --- A High Capacity Encoding Scheme for FAMs --- p.90 / Chapter 5.5 --- Memory Capacity --- p.91 / Chapter 5.6 --- Rule Modification --- p.93 / Chapter 5.7 --- Inference Performance --- p.99 / Chapter 5.8 --- Concluding Remarks --- p.104 / Chapter 6. --- Capacity Analysis of Fuzzy Relational Neural Systems --- p.105 / Chapter 6.1 --- Introduction --- p.105 / Chapter 6.2 --- Fuzzy Relational Equations and Fuzzy Relational Neural Systems --- p.107 / Chapter 6.3 --- Solving a System of Fuzzy Relational Equations --- p.109 / Chapter 6.4 --- New Solvable Conditions --- p.112 / Chapter 6.4.1 --- Max-t Fuzzy Relational Equations --- p.112 / Chapter 6.4.2 --- Min-s Fuzzy Relational Equations --- p.117 / Chapter 6.5 --- Approximate Resolution --- p.119 / Chapter 6.6 --- System Capacity --- p.123 / Chapter 6.7 --- Inference Performance --- p.125 / Chapter 6.8 --- Concluding Remarks --- p.127 / Chapter 7. --- Structure and Parameter Identifications of Fuzzy Relational Neural Systems --- p.129 / Chapter 7.1 --- Introduction --- p.129 / Chapter 7.2 --- Modelling Nonlinear Dynamic Systems by Fuzzy Relational Equations --- p.131 / Chapter 7.3 --- A General FRNS Identification Algorithm --- p.138 / Chapter 7.4 --- An Evolutionary Computation Approach to Structure and Parameter Identifications --- p.139 / Chapter 7.4.1 --- Guided Evolutionary Simulated Annealing --- p.140 / Chapter 7.4.2 --- An Evolutionary Identification (EVIDENT) Algorithm --- p.143 / Chapter 7.5 --- Simulation Results --- p.146 / Chapter 7.6 --- Concluding Remarks --- p.158 / Chapter 8. --- Conclusions --- p.159 / Chapter 8.1 --- Summary of Contributions --- p.160 / Chapter 8.1.1 --- Fuzzy Competitive Learning --- p.160 / Chapter 8.1.2 --- Capacity Analysis of FAM and FRNS --- p.160 / Chapter 8.1.3 --- Numerical Identification of FRNS --- p.161 / Chapter 8.2 --- Further Investigations --- p.162 / Appendix A Publication List of the Candidate --- p.164 / BIBLIOGRAPHY --- p.166