Designing Unsupervised Hierarchical Fuzzy Logic Systems

Designing Unsupervised Hierarchical Fuzzy Logic Systems

M. Mohammadian (University of Canberra, Australia)
Copyright: © 2009 |Pages: 8
DOI: 10.4018/978-1-59904-849-9.ch070
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Abstract

Systems such as robotic systems and systems with large input-output data tend to be difficult to model using mathematical techniques. These systems have typically high dimensionality and have degrees of uncertainty in many parameters. Artificial intelligence techniques such as neural networks, fuzzy logic, genetic algorithms and evolutionary algorithms have created new opportunities to solve complex systems. Application of fuzzy logic [Bai, Y., Zhuang H. and Wang, D. (2006)] in particular, to model and solve industrial problems is now wide spread and has universal acceptance. Fuzzy modelling or fuzzy identification has numerous practical applications in control, prediction and inference. It has been found useful when the system is either difficult to predict and or difficult to model by conventional methods. Fuzzy set theory provides a means for representing uncertainties. The underlying power of fuzzy logic is its ability to represent imprecise values in an understandable form. The majority of fuzzy logic systems to date have been static and based upon knowledge derived from imprecise heuristic knowledge of experienced operators, and where applicable also upon physical laws that governs the dynamics of the process. Although its application to industrial problems has often produced results superior to classical control, the design procedures are limited by the heuristic rules of the system. It is simply assumed that the rules for the system are readily available or can be obtained. This implicit assumption limits the application of fuzzy logic to the cases of the system with a few parameters. The number of parameters of a system could be large. The number of fuzzy rules of a system is directly dependent on these parameters. As the number of parameters increase, the number of fuzzy rules of the system grows exponentially. Genetic Algorithms can be used as a tool for the generation of fuzzy rules for a fuzzy logic system. This automatic generation of fuzzy rules, via genetic algorithms, can be categorised into two learning techniques, supervised and unsupervised. In this paper unsupervised learning of fuzzy rules of hierarchical and multi-layer fuzzy logic control systems are considered. In unsupervised learning there is no external teacher or critic to oversee the learning process. In other words, there are no specific examples of the function to be learned by the system. Rather, provision is made for a task-independent measure of the quality or representation that the system is required to learn. That is the system learns statistical regularities of the input data and it develops the ability to learn the feature of the input data and thereby create new classes automatically [Mohammadian, M., Nainar, I. and Kingham, M. (1997)]. To perform unsupervised learning, a competitive learning strategy may be used. The individual strings of genetic algorithms compete with each other for the “opportunity” to respond to features contained in the input data. In its simplest form, the system operates in accordance with the strategy that ‘the fittest wins and survives’. That is the individual chromosome in a population with greatest fitness ‘wins’ the competition and gets selected for the genetic algorithms operations (cross-over and mutation). The other individuals in the population then have to compete with fit individual to survive. The diversity of the learning tasks shown in this paper indicates genetic algorithm’s universality for concept learning in unsupervised manner. A hybrid integrated architecture incorporating fuzzy logic and genetic algorithm can generate fuzzy rules for problems requiring supervised or unsupervised learning. In this paper only unsupervised learning of fuzzy logic systems is considered. The learning of fuzzy rules and internal parameters in an unsupervised manner is performed using genetic algorithms. Simulations results have shown that the proposed system is capable of learning the control rules for hierarchical and multi-layer fuzzy logic systems. Application areas considered are, hierarchical control of a network of traffic light control and robotic systems. A first step in the construction of a fuzzy logic system is to determine which variables are fundamentally important. Any number of these decision variables may appear, but the more that are used, the larger the rule set that must be found. It is known [Raju, S., Zhou J. and Kisner, R. A. (1990), Raju G. V. S. and Zhou, J. (1993), Kingham, M., Mohammadian, M, and Stonier, R. J. (1998)], that the total number of rules in a system is an exponential function of the number of system variables. In order to design a fuzzy system with the required accuracy, the number of rules increases exponentially with the number of input variables and its associated fuzzy sets for the fuzzy logic system. A way to avoid the explosion of fuzzy rule bases in fuzzy logic systems is to consider Hierarchical Fuzzy Logic Control (HFLC) [Raju G. V. S. and Zhou, J. (1993)]. A learning approach based on genetic algorithms [Goldberg, D. (1989)] is discussed in this paper for the determination of the rule bases of hierarchical fuzzy logic systems.
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Introduction

Systems such as robotic systems and systems with large input-output data tend to be difficult to model using mathematical techniques. These systems have typically high dimensionality and have degrees of uncertainty in many parameters. Artificial intelligence techniques such as neural networks, fuzzy logic, genetic algorithms and evolutionary algorithms have created new opportunities to solve complex systems. Application of fuzzy logic [Bai, Y., Zhuang H. and Wang, D. (2006)] in particular, to model and solve industrial problems is now wide spread and has universal acceptance. Fuzzy modelling or fuzzy identification has numerous practical applications in control, prediction and inference. It has been found useful when the system is either difficult to predict and or difficult to model by conventional methods. Fuzzy set theory provides a means for representing uncertainties. The underlying power of fuzzy logic is its ability to represent imprecise values in an understandable form. The majority of fuzzy logic systems to date have been static and based upon knowledge derived from imprecise heuristic knowledge of experienced operators, and where applicable also upon physical laws that governs the dynamics of the process.

Although its application to industrial problems has often produced results superior to classical control, the design procedures are limited by the heuristic rules of the system. It is simply assumed that the rules for the system are readily available or can be obtained. This implicit assumption limits the application of fuzzy logic to the cases of the system with a few parameters. The number of parameters of a system could be large. The number of fuzzy rules of a system is directly dependent on these parameters. As the number of parameters increase, the number of fuzzy rules of the system grows exponentially.

Genetic Algorithms can be used as a tool for the generation of fuzzy rules for a fuzzy logic system. This automatic generation of fuzzy rules, via genetic algorithms, can be categorised into two learning techniques, supervised and unsupervised. In this paper unsupervised learning of fuzzy rules of hierarchical and multi-layer fuzzy logic control systems are considered. In unsupervised learning there is no external teacher or critic to oversee the learning process. In other words, there are no specific examples of the function to be learned by the system. Rather, provision is made for a task-independent measure of the quality or representation that the system is required to learn. That is the system learns statistical regularities of the input data and it develops the ability to learn the feature of the input data and thereby create new classes automatically [Mohammadian, M., Nainar, I. and Kingham, M. (1997)].

To perform unsupervised learning, a competitive learning strategy may be used. The individual strings of genetic algorithms compete with each other for the “opportunity” to respond to features contained in the input data. In its simplest form, the system operates in accordance with the strategy that ‘the fittest wins and survives’. That is the individual chromosome in a population with greatest fitness ‘wins’ the competition and gets selected for the genetic algorithms operations (cross-over and mutation). The other individuals in the population then have to compete with fit individual to survive.

The diversity of the learning tasks shown in this paper indicates genetic algorithm’s universality for concept learning in unsupervised manner. A hybrid integrated architecture incorporating fuzzy logic and genetic algorithm can generate fuzzy rules for problems requiring supervised or unsupervised learning. In this paper only unsupervised learning of fuzzy logic systems is considered. The learning of fuzzy rules and internal parameters in an unsupervised manner is performed using genetic algorithms. Simulations results have shown that the proposed system is capable of learning the control rules for hierarchical and multi-layer fuzzy logic systems. Application areas considered are, hierarchical control of a network of traffic light control and robotic systems.

Key Terms in this Chapter

Unsupervised Learning: In unsupervised learning there is no external teacher or critic to oversee the learning process. In other words, there are no specific examples of the function to be learned by the system. Rather, provision is made for a task-independent measure of the quality or representation that the system is required to learn. That is the system learns statistical regularities of the input data and it develops the ability to learn the feature of the input data and thereby create new classes automatically

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

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

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

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

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 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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