M. Mohammadian (University of Canberra, Australia)

DOI: 10.4018/978-1-59904-849-9.ch221

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TopConventionally modelling and simulation of complex nonlinear systems has been to construct a mathematical model and examine the system’s evolution or its control. This kind of approach can fail for many of the very large non-linear and complex systems being currently studied. With the invention of new advanced high-speed computers and the application of artificial intelligence paradigms new techniques have become available. Particularly neural networks and fuzzy logic for nonlinear modelling and genetic algorithms [Goldberg, D. (1989)] and evolutionary algorithms for optimisation methods have created new opportunities to solve complex systems [Bai, Y., Zhuang H. and Wang, D. (2006)].

This paper considers issues in design of multi-layer and hierarchical fuzzy logic systems. It proposes a decomposition technique for complex systems into hierarchical and multi-layered fuzzy logic sub-systems. The learning of fuzzy rules and internal parameters in a supervised manner is performed using genetic algorithms. The decomposition of complex nonlinear systems into hierarchical and multi-layered fuzzy logic sub-systems reduces greatly the number of fuzzy rules to be defined and improves the learning speed for such systems. In this paper a method for combining subsystems to create a hierarchical and multilayer fuzzy logic system is also described. Application areas considered are - the prediction of interest rate, unemployment rate predication and electricity usage prediction.

Genetic Algorithms can be used as a tool for design and generation of fuzzy rules for a fuzzy logic system. This automatic design and generation of fuzzy rules, via genetic algorithms, can be categorised into two learning techniques namely, supervised and unsupervised. In supervised learning there are two distinct phases to the operation. In the first phase each individual is assessed based on the input signal that is propagated through the system producing output respond. The actual respond produced is then compared with a desired response, generating error signals that are then used as the fitness for the individual in the population of genetic algorithms. Supervised learning has successfully applied to solve some difficult problems. In this paper design and development of a genetic algorithm based supervised learning for fuzzy models with application to several problems is considered. A hybrid integrated architecture incorporating fuzzy logic and genetic algorithm can generate fuzzy rules that can be used in a fuzzy logic system for modelling, control and prediction.

Fuzzy logic systems typically have a knowledge base consisting of a set of rules of the form

If (*x _{1}* is

Then (z* _{1}* is

Fuzzy Logic: Fuzzy sets and Fuzzy Logic were introduced in 1965 by Lotfi Zadeh as a new way to represent vagueness in applications. They are a generalisation of sets in conventional set theory. Fuzzy Logic (FL) aims at modelling imprecise models of reasoning, such as common sense reasoning for uncertain complex processes. A system for representing the meaning of lexically imprecise proposition in natural language structure through the proposition being represented as fuzzy constraints on a variable is provided. Fuzzy logic controllers have been applied to many nonlinear control systems successfully. Linguistic rather than crisp numerical rules are used to control the processes.

Supervised Learning: A learning method in which there are two distinct phases to the operation. In the first phase each possible solution to a problem is assessed based on the input signal that is propagated through the system producing output respond. The actual respond produced is then compared with a desired response, generating error signals that are then used as a guide to solve the given problems using supervised learning algorithms.

Fuzzy Rule Base (Fuzzy If-Then rules): Fuzzy If-Then or fuzzy conditional statements are expressions of the form “If A Then B”, where A and B are labels of fuzzy sets characterised by appropriate membership functions. Due to their concise form, fuzzy If-Then rules are often employed to capture the imprecise modes of reasoning that play an essential role in the human ability to make decision in an environment of uncertainty and imprecision. The set of If-Then rules relate to a fuzzy logic system that are stored together is called a Fuzzy Rule Base.

Hierarchical Fuzzy Logic Systems: The idea of hierarchical fuzzy logic control systems is to put the input variables into a collection of low-dimensional fuzzy logic control systems, instead of creating a single high dimensional rule base for a fuzzy logic control system. Each low-dimensional fuzzy logic control system constitutes a level in the hierarchical fuzzy logic control system. Hierarchical fuzzy logic control is one approach to avoid rule explosion problem. It has the property that the number of rules needed to construct the fuzzy system increases only linearly with the number of variables in the system

Fusing Variables: Fusing variables is a method for reducing the number of rules in a fuzzy rule base. The variables are fused (combined) together before input into the inference engine, thereby reducing the number of rules in the knowledge base.

Genetic Algorithms: Genetic Algorithms (GAs) are algorithms that use operations found in natural genetics to guide their way through a search space and are increasingly being used in the field of optimisation. The robust nature and simple mechanics of genetic algorithms make them inviting tools for search learning and optimization. Genetic algorithms are based on computational models of fundamental evolutionary processes such as selection, recombination and mutation

Genetic Algorithms Components: In its simplest form, a genetic algorithm has the following components, 1. Fitness- A positive measure of utility, called fitness, is determined for individuals in a population. This fitness value is a quantitative measure of how well a given individual compares to others in the population. 2. Selection- Population individuals are assigned a number of copies in a mating pool that is used to construct a new population. The higher a population individual’s fitness, the more copies in the mating pool it receives. 3. Recombination- Individuals from the mating pool are recombined to form new individuals, called children. A common recombination method is one-point crossover. 4. Mutation- Each individual is mutated with some small probability << 1.0. Mutation is a mechanism for maintaining diversity in the population.

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