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Type-2 Fuzzy Logic: Theory and Applications

verfasst von: Oscar Castillo, Patricia Melin

Verlag: Springer Berlin Heidelberg

Buchreihe : Studies in Fuzziness and Soft Computing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

We describe in this book, new methods for building intelligent systems using type-2 fuzzy logic and soft computing techniques. Soft Computing (SC) consists of several computing paradigms, including type-1 fuzzy logic, neural networks, and genetic algorithms, which can be used to create powerful hybrid intelligent systems. In this book, we are extending the use of fuzzy logic to a higher order, which is called type-2 fuzzy logic. Combining type-2 fuzzy logic with traditional SC techniques, we can build powerful hybrid intelligent systems that can use the advantages that each te- nique offers. We consider in this book the use of type-2 fuzzy logic and traditional SC techniques to solve pattern recognition problems in real-world applications. We c- sider in particular the problems of face, fingerprint and voice recognition. We also consider the problem of recognizing a person by integrating the information given by the face, fingerprint and voice of the person. Other types of applications solved with type-2 fuzzy logic and SC techniques, include intelligent control, intelligent manuf- turing, and adaptive noise cancellation. This book is intended to be a major reference for scientists and engineers interested in applying type-2 fuzzy logic for solving problems in pattern recognition, intelligent control, intelligent manufacturing, robotics and automation.

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Inhaltsverzeichnis

Frontmatter

1 Introduction to Type-2 Fuzzy Logic

Contents

We describe in this book, new methods for building intelligent systems using type-2 fuzzy logic and soft computing techniques. Soft Computing (SC) consists of several computing paradigms, including type-1 fuzzy logic, neural networks, and genetic algorithms, which can be used to create powerful hybrid intelligent systems. In this book, we are extending the use of fuzzy logic to a higher order, which is called type-2 fuzzy logic. Combining type-2 fuzzy logic with traditional SC techniques, we can build powerful hybrid intelligent systems that can use the advantages that each technique offers. We consider in this book the use of type-2 fuzzy logic and traditional SC techniques to solve pattern recognition problems in real-world applications. We consider in particular the problems of face, fingerprint and voice recognition. We also consider the problem of recognizing a person by integrating the information given by the face, fingerprint and voice of the person. Other types of applications solved with type-2 fuzzy logic and SC techniques, include intelligent control, intelligent manufacturing, and adaptive noise cancellation.

Oscar Castillo, Patricia Melin

2 Type-1 Fuzzy Logic

Contents

This chapter introduces the basic concepts, notation, and basic operations for the type-1 fuzzy sets that will be needed in the following chapters. Type-2 fuzzy sets as well as their operations will be discussed in the next chapter. For this reason, in this chapter we will focus only on type-1 fuzzy logic. Since research on fuzzy set theory has been underway for over 30 years now, it is practically impossible to cover all aspects of current developments in this area. Therefore, the main goal of this chapter is to provide an introduction to and a summary of the basic concepts and operations that are relevant to the study of type-1 fuzzy sets. We also introduce in this chapter the definition of linguistic variables and linguistic values and explain how to use them in type-1 fuzzy rules, which are an efficient tool for quantitative modeling of words or sentences in a natural or artificial language. By interpreting fuzzy rules as fuzzy relations, we describe different schemes of fuzzy reasoning, where inference procedures based on the concept of the compositional rule of inference are used to derive conclusions from a set of fuzzy rules and known facts. Fuzzy rules and fuzzy reasoning are the basic components of fuzzy inference systems, which are the most important modeling tool, based on fuzzy set theory.

Oscar Castillo, Patricia Melin

3 Type-2 Fuzzy Logic

Contents

We introduce in this chapter a new area in fuzzy logic, which is called type-2 fuzzy logic. Basically, a type-2 fuzzy set is a set in which we also have uncertainty about the membership function. Of course, type-2 fuzzy systems consist of fuzzy if-then rules, which contain type-2 fuzzy sets. We can say that type-2 fuzzy logic is a generalization of conventional fuzzy logic (type-1) in the sense that uncertainty is not only limited to the linguistic variables but also is present in the definition of the membership functions.

Oscar Castillo, Patricia Melin

4 A Method for Type-2 Fuzzy Inference in Control Applications

Contents

A novel method of type 2 fuzzy logic inference is presented in this chapter. The method is highly efficient regarding computational time and implementation effort. Type-2 input membership functions are optimized using the Human Evolutionary Model (HEM) considering as the objective function the Integral of Squared Error at the controllers output. Statistical tests were achieved considering how the error at the controller’s output is diminished in presence of uncertainty, demonstrating that the proposed method outperforms an optimized traditional type-2 fuzzy controller for the same test conditions.

Oscar Castillo, Patricia Melin

5 Design of Intelligent Systems with Interval Type-2 Fuzzy Logic

Contents

Uncertainty is an inherent part of intelligent systems used in real-world applications. The use of new methods for handling incomplete information is of fundamental importance. Type-1 fuzzy sets used in conventional fuzzy systems cannot fully handle the uncertainties present in intelligent systems. Type-2 fuzzy sets that are used in type-2 fuzzy systems can handle such uncertainties in a better way because they provide us with more parameters. This chapter deals with the design of intelligent systems using interval type-2 fuzzy logic for minimizing the effects of uncertainty produced by the instrumentation elements, environmental noise, etc. Experimental results include simulations of feedback control systems for non-linear plants using type-1 and type-2 fuzzy logic controllers; a comparative analysis of the systems’ response is performed, with and without the presence of uncertainty.

Oscar Castillo, Patricia Melin

6 Method for Response Integration in Modular Neural Networks with Type-2 Fuzzy Logic

Contents

We describe in this chapter a new method for response integration in modular neural networks using type-2 fuzzy logic. The modular neural networks were used in human person recognition. Biometric authentication is used to achieve person recognition. Three biometric characteristics of the person are used: face, fingerprint, and voice. A modular neural network of three modules is used. Each module is a local expert on person recognition based on each of the biometric measures. The response integration method of the modular neural network has the goal of combining the responses of the modules to improve the recognition rate of the individual modules. We show in this chapter the results of a type-2 fuzzy approach for response integration that improves performance over type-1 fuzzy logic approaches.

Oscar Castillo, Patricia Melin

7 Type-2 Fuzzy Logic for Improving Training Data and Response Integration in Modular Neural Networks for Image Recognition

Contents

The combination of Soft Computing techniques allows the improvement of intelligent systems with different hybrid approaches. In this work we consider two parts of a Modular Neural Network for image recognition, where a Type-2 Fuzzy Inference System (FIS 2) makes a great difference. The first FIS 2 is used for feature extraction in training data, and the second one to find the ideal parameters for the integration method of the modular neural network. Once again Fuzzy Logic is shown to be a tool that can help improve the results of a neural system, when facilitating the representation of the human perception.

Oscar Castillo, Patricia Melin

8 Fuzzy Inference Systems Type-1 and Type-2 for Digital Images Edge Detection

Contents

Edges detection in digital images is a problem that has been solved by means of the application of different techniques from digital signal processing, also the combination of some of these techniques with Fuzzy Inference System (FIS) has been experienced. In this chapter a new FIS Type-2 method is implemented for the detection of edges and the results of three different techniques for the same intention are compared.

Oscar Castillo, Patricia Melin

9 Systematic Design of a Stable Type-2 Fuzzy Logic Controller

Contents

Stability is one of the more important aspects in the traditional knowledge of Automatic Control. Type-2 Fuzzy Logic is an emerging and promising area for achieving Intelligent Control (in this case, Fuzzy Control). In this chapter we use the Fuzzy Lyapunov Synthesis as proposed by Margaliot to build a Lyapunov Stable Type-1 Fuzzy Logic Control System, and then we make an extension from a Type-1 to a Type-2 Fuzzy Logic Control System, ensuring the stability on the control system and proving the robustness of the corresponding fuzzy controller.

Oscar Castillo, Patricia Melin

10 Experimental Study of Intelligent Controllers Under Uncertainty Using Type-1 and Type-2 Fuzzy Logic

Contents

Uncertainty is an inherent part in controllers used for real-world applications. The use of new methods for handling incomplete information is of fundamental importance in engineering applications. This chapter deals with the design of controllers using type-2 fuzzy logic for minimizing the effects of uncertainty produced by the instrumentation elements. We simulated type-1 and type-2 fuzzy logic controllers to perform a comparative analysis of the systems’ response, in the presence of uncertainty.

Oscar Castillo, Patricia Melin

11 Evolutionary Optimization of Interval Type-2 Membership Functions Using the Human Evolutionary Model

Contents

Uncertainty is an inherent part in controllers used for real-world applications. The use of new methods for handling incomplete information is of fundamental importance in engineering applications. We simulated the effects of uncertainty produced by the instrumentation elements in type-1 and type-2 fuzzy logic controllers to perform a comparative analysis of the systems’ response, in the presence of uncertainty. We are presenting an innovative idea to optimize interval type-2 membership functions using an average of two type-1 systems with the Human Evolutionary Model, we are showing comparative results of the optimized proposed method. We found that the optimized membership functions for the inputs of a type-2 system increases the performance of the system for high noise levels.

Oscar Castillo, Patricia Melin

12 Design of Fuzzy Inference Systems with the Interval Type-2 Fuzzy Logic Toolbox

Contents

This chapter presents the development and design of a graphical user interface and a command line programming Toolbox for construction, edition and simulation of Interval Type-2 Fuzzy Inference Systems. The Interval Type-2 Fuzzy Logic System Toolbox (IT2FLS), is an environment for interval type-2 fuzzy logic inference system development. Tools that cover the different phases of the fuzzy system design process, from the initial description phase, to the final implementation phase, constitute the Toolbox. The Toolbox’s best qualities are the capacity to develop complex systems and the flexibility that allows the user to extend the availability of functions for working with the use of type-2 fuzzy operators, linguistic variables, interval type-2 membership functions, defuzzification methods and the evaluation of Interval Type-2 Fuzzy Inference Systems.

Oscar Castillo, Patricia Melin

13 Intelligent Control of the Pendubot with Interval Type-2 Fuzzy Logic

Contents

We describe in this chapter adaptive model-based control of non-linear plants using type-2 fuzzy logic and neural networks. First, the general concept of adaptive model-based control is described. Second, the use of type-2 fuzzy logic for adaptive control is described. Third, a neuro-fuzzy approach is proposed to learn the parameters of the fuzzy system for control. A specific non-linear plant was used to simulate the hybrid approach for adaptive control. The specific plant was also used as test bed in the experiments. The non-linear plant that was considered is the "Pendubot", which is a non-linear plant similar to the two-link robot arm. The results of the type-2 fuzzy logic approach for control were good, both in accuracy and efficiency.

Oscar Castillo, Patricia Melin

14 Automated Quality Control in Sound Speakers Manufacturing Using a Hybrid Neuro-fuzzy-Fractal Approach

Contents

We describe in this chapter the application of type-2 fuzzy logic to the problem of automated quality control in sound speaker manufacturing. Traditional quality control has been done by manually checking the quality of sound after production. This manual checking of the speakers is time consuming and occasionally was the cause of error in quality evaluation. For this reason, we developed an intelligent system for automated quality control in sound speaker manufacturing. The intelligent system has a type-2 fuzzy rule base containing the knowledge of human experts in quality control. The parameters of the fuzzy system are tuned by applying neural networks using, as training data, a real time series of measured sounds as given by good sound speakers. We also use the fractal dimension as a measure of the complexity of the sound signal.

Oscar Castillo, Patricia Melin

15 A New Approach for Plant Monitoring Using Type-2 Fuzzy Logic and Fractal Theory

Contents

We describe in this chapter a new approach for plant monitoring and diagnostics using type-2 fuzzy logic and fractal theory. The concept of the fractal dimension is used to measure the complexity of the time series of relevant variables for the process. A set of type-2 fuzzy rules is used to represent the knowledge for monitoring the process. In the type-2 fuzzy rules, the fractal dimension is used as a linguistic variable to help in recognizing specific patterns in the measured data. The fuzzy-fractal approach has been applied before in problems of financial time series prediction and for other types of problems, but now it is proposed to the monitoring of plants using type-2 fuzzy logic. We also compare the results of the type-2 fuzzy logic approach with the results of using only a traditional type-1 fuzzy logic approach. Experimental results show a significant improvement in the monitoring ability with the type-2 fuzzy logic approach.

Oscar Castillo, Patricia Melin

16 Intelligent Control of Autonomous Robotic Systems Using Interval Type-2 Fuzzy Logic and Genetic Algorithms

Contents

We develop a tracking controller for the dynamic model of unicycle mobile robot by integrating a kinematic controller and a torque controller based on Fuzzy Logic Theory. Computer simulations are presented confirming the performance of the tracking controller and its application to different navigation problems.

Oscar Castillo, Patricia Melin

17 Adaptive Noise Cancellation Using Type-2 Fuzzy Logic and Neural Networks

Contents

We describe in this chapter the application of type-2 fuzzy logic for achieving adaptive noise cancellation. The objective of adaptive noise cancellation is to filter out an interference component by identifying a model between a measurable noise source and the corresponding un-measurable interference. In this chapter, we propose the use of type-2 fuzzy logic to find this model. The use of type-2 fuzzy logic is justified due to the high level of uncertainty of the process, which makes difficult to find appropriate parameter values for the membership functions.

Oscar Castillo, Patricia Melin

Backmatter

Titel: Type-2 Fuzzy Logic: Theory and Applications
verfasst von: Oscar Castillo
Patricia Melin
Copyright-Jahr: 2008
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-540-76284-3
Print ISBN: 978-3-540-76283-6
DOI: https://doi.org/10.1007/978-3-540-76284-3

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