Fuzzy Chaotic Neural Networks

Fuzzy Chaotic Neural Networks

Tang Mo (Automation College, Harbin Engineering University, China), Wang Kejun (Automation College, Harbin Engineering University, China), Zhang Jianmin (Automation College, Harbin Engineering University, China) and Zheng Liying (Automation College, Harbin)
DOI: 10.4018/978-1-60566-310-4.ch024
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Abstract

An understanding of the human brain’s local function has improved in recent years. But the cognition of human brain’s working process as a whole is still obscure. Both fuzzy logic and dynamic chaos are internal features of the human brain. Therefore, to fuse artificial neural networks, fuzzy logic and dynamic chaos together to constitute fuzzy chaotic neural networks is a novel method. This chapter is focused on the new ways of fuzzy neural networks construction and its application based on the existing achievement in this field. Four types of fuzzy chaotic neural networks are introduced, namely chaotic recurrent fuzzy neural networks, cooperation fuzzy chaotic neural networks, fuzzy number chaotic neural networks and self-evolution fuzzy chaotic neural networks. Chaotic recurrent fuzzy neural networks model is developed based on existing recurrent fuzzy neural networks through introducing chaos mapping into the membership layer. As it is a dynamic system, the input of neuron not only processes the information of former monument but also contains chaos maps information which is provided by dynamic chaos. Cooperation fuzzy chaotic neural network is proposed on the basis of simplified T-S fuzzy chaotic neural networks and Aihara chaotic neuron. It realizes fuzzy reasoning process by a neural network structure in which the rule inference part is realized by chaotic neural networks. Then enlightened by fuzzy number neural networks we propose a fuzzy number chaotic neuron, which is obtained by blurring the Aihara chaotic neuron. Using these neurons to construct fuzzy number chaotic neural networks, the mathematical model and weight updating rules are also given. At last, a self-evolution fuzzy chaotic neural network is proposed according to the principle of self-evolution network, which unifies the fuzzy Hopfield neural network constitution method.
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Introduction

There is appreciable understanding of some partial functions of the human brain. The researches of perceptrons, visual processing network, and memory and so on, have attained certain levels of success. Unfortunately despite these successes the overall function of the human brain remains a real challenge to understand. At present scientists have already accumulated massive knowledge of basic and essential facts about brain composition, brain contour and cerebrum function, but are still unable to explain substantively, the question of brain information processing.

But the integrated function is in no way a simple combination the partial function. The consciousness and cognition process of the brain involves a complex dynamic system to carry on the massive neuron activity. The fact that people do not have a complete understanding of the human brain and work process, underscores a need for qualitative leap in this research (Zhu, D.Q., 2004).

It is well known, that neural network is an attempt to simulate the human brain’s structure and primary function. Fuzziness is a remarkable characteristic of human brain. The synergy of neural network and the fuzzy theory helps to address more complex questions in wider application domains with a solution model usually called the fuzzy neural network.

Chaos has been discovered to be a characteristic of the dynamics present in the brain. In the cranial nerve system, from the microscopic neuron and neural network, to the macroscopic brain wave and the brain magnetic wave, chaos were discovered in two aspects (Huang, R. S., 2000; Wang, Y. N, Yu, Q. M., & Yuan, X. F., 2006).Chaos theory could help understand certain irregular activities in the brain, thus the chaos dynamics provide people a new turning point to study the neural network. The chaos phenomenon is has inherently a non-linear dynamics, and the neural network is also a highly non-linear dynamics system, so that both have a close correlation.

At present, the fuzzy neural network technology have been well developed, and widely applied in many kinds of domains. The chaos dynamics and the chaos neural network technology is an exciting emerging research area which yielded encouraging results from theory to application. From the existed literature, it can be seen that the proposed fuzzy neural network models (whether the static or dynamic models) do not consider the chaos characteristic of actual biological neural network (Liu, C. J., Liao, X. Z., & Zhang, Y. H. 2000; Juang, C. F., 2004; Yang, G., & Meng, J. E., 2005; Abdulhamit, S., 2006; Theocharis, J. B., 2006; Gu, L. L., & Deng, Z. L., 2006; Shashi, K., Sanjeev, K., Prakash, Ravi, S., Tiwari, M. K., & Shashi B. K., 2007). The chaotic neural network technology stems from chaos dynamic do not consider the fuzzy characteristic of actual biological neural network, and cannot process the fuzzy information. From the exist literature, the research of fuse fuzzy logic, chaos and artificial neural networks is extremely few at present.

Key Terms in this Chapter

Fuzzy Number Chaotic Neural Networks: The convexity of fuzzy number described by figure1 stated for: make a -cut parallel to x axis (), generate interval, where[INSERT FIGURE 002], are abscissa of cut point, and that convexity refer to .Fuzzy number neural network is an extension of general neural networks; its input and output along with weight are all fuzzy numbers.

Cooperation Fuzzy Chaotic Neural Networks: It is an improvement of T-S fuzzy neural networks by introducing chaotic neurons or chaotic neural networks. The rule conclusion layer is constituted by chaotic neural networks, which could be one layer or multi-layers.

Fuzzy Chaotic Neural Networks: It is a new network which combine fuzzy logic, chaos and neural networks together. It has fuzzy reasoning ability, auto-adapted, self-learning as well as chaos search ability, in order to enhance information-handling capacity.

Self-Evolution Neural Networks: In the mathematical model of self-evolution neural network, the inspiring function is a chaotic odd-symmetric nonmonotonic function differing from normal neural network. It has periodic trait and chaos trait under certain circumstances.

Chaotic Recurrent Fuzzy Neural Network: It is based on recurrent fuzzy neural networks, and has four layers, namely input layer, membership function layer, rule layer and output layer. Chaotic mapping is introduced into the membership layer, via addition of chaotic neurons into the recurrent fuzzy neural networks.

Self-Evolution Fuzzy Chaotic Neural Networks: It is proposed according to the principle of self-evolution network, and unifies the fuzzy Hopfield neural network constitution method. It can work under two kind of active status and completely different function.

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Table of Contents
Foreword
Lipo Wang
Preface
Hongwei Mo
Chapter 1
Fabio Freschi, Carlos A. Coello Coello, Maurizio Repetto
This chapter aims to review the state of the art in algorithms of multiobjective optimization with artificial immune systems (MOAIS). As it will be... Sample PDF
Multiobjective Optimization and Artificial Immune Systems: A Review
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Chapter 2
Jun Chen, Mahdi Mahfouf
The primary objective of this chapter is to introduce Artificial Immune Systems (AIS) as a relatively new bio-inspired optimization technique and to... Sample PDF
Artificial Immune Systems as a Bio-Inspired Optimization Technique and Its Engineering Applications
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Chapter 3
Licheng Jiao, Maoguo Gong, Wenping Ma
Many immue-inspired algorithms are based on the abstractions of one or several immunology theories, such as clonal selection, negative selection... Sample PDF
An Artificial Immune Dynamical System for Optimization
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Chapter 4
Malgorzata Lucinska, Slawomir T. Wierzchon
Multi-agent systems (MAS), consist of a number of autonomous agents, which interact with one-another. To make such interactions successful, they... Sample PDF
An Immune Inspired Algorithm for Learning Strategies in a Pursuit-Evasion Game
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Chapter 5
Luis Fernando Niño Vasquez, Fredy Fernando Muñoz Mopan, Camilo Eduardo Prieto Salazar, José Guillermo Guarnizo Marín
Artificial Immune Systems (AIS) have been widely used in different fields such as robotics, computer science, and multi-agent systems with high... Sample PDF
Applications of Artificial Immune Systems in Agents
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Chapter 6
Xingquan Zuo
Inspired from the robust control principle, a robust scheduling method is proposed to solve uncertain scheduling problems. The uncertain scheduling... Sample PDF
An Immune Algorithm Based Robust Scheduling Methods
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Chapter 7
Fabio Freschi, Maurizio Repetto
The increasing cost of energy and the introduction of micro-generation facilities and the changes in energy production systems require new... Sample PDF
Artificial Immune System in the Management of Complex Small Scale Cogeneration Systems
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Chapter 8
Krzysztof Ciesielski, Mieczyslaw A. Klopotek, Slawomir T. Wierzchon
In this chapter the authors discuss an application of an immune-based algorithm for extraction and visualization of clusters structure in large... Sample PDF
Applying the Immunological Network Concept to Clustering Document Collections
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Chapter 9
Xiangrong Zhang, Fang Liu
The problem of feature selection is fundamental in various tasks like classification, data mining, image processing, conceptual learning, and so on.... Sample PDF
Feature Selection Based on Clonal Selection Algorithm: Evaluation and Application
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Chapter 10
Yong-Sheng Ding, Xiang-Feng Zhang, Li-Hong Ren
Future Internet should be capable of extensibility, survivability, mobility, and adaptability to the changes of different users and network... Sample PDF
Immune Based Bio-Network Architecture and its Simulation Platform for Future Internet
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Chapter 11
Tao Gong
Static Web immune system is an important applicatiion of artificial immune system, and it is also a good platform to develop new immune computing... Sample PDF
A Static Web Immune System and Its Robustness Analysis
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Chapter 12
Alexander O. Tarakanov
Based on mathematical models of immunocomputing, this chapter describes an approach to spatio-temporal forecast (STF) by intelligent signal... Sample PDF
Immunocomputing for Spatio-Temporal Forecast
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Chapter 13
Fu Dongmei
In engineering application, the characteristics of the control system are entirely determined by the system controller once the controlled object... Sample PDF
Research of Immune Controllers
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Chapter 14
Xiaojun Bi
In fact, image segmentation can be regarded as a constrained optimization problem, and a series of optimization strategies can be used to complete... Sample PDF
Immune Programming Applications in Image Segmentation
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Chapter 15
Xin Wang, Wenjian Luo, Zhifang Li, Xufa Wang
A hardware immune system for the error detection of MC8051 IP core is designed in this chapter. The binary string to be detected by the hardware... Sample PDF
A Hardware Immune System for MC8051 IP Core
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Chapter 16
Mark Burgin, Eugene Eberbach
There are different models of evolutionary computations: genetic algorithms, genetic programming, etc. This chapter presents mathematical... Sample PDF
On Foundations of Evolutionary Computation: An Evolutionary Automata Approach
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Chapter 17
Terrence P. Fries
Path planning is an essential component in the control software for an autonomous mobile robot. Evolutionary strategies are employed to determine... Sample PDF
Evolutionary Path Planning for Robot Navigation Under Varying Terrain Conditions
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Chapter 18
Konstantinos Konstantinidis, Georgios Ch. Sirakoulis, Ioannis Andreadis
The aim of this chapter is to provide the reader with a Content Based Image Retrieval (CBIR) system which incorporates AI through ant colony... Sample PDF
Ant Colony Optimization for Use in Content Based Image Retrieval
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Chapter 19
Miroslav Bursa, Lenka Lhotska
The chapter concentrates on the use of swarm intelligence in data mining. It focuses on the problem of medical data clustering. Clustering is a... Sample PDF
Ant Colonies and Data Mining
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Chapter 20
Bo-Suk Yang
This chapter describes a hybrid artificial life optimization algorithm (ALRT) based on emergent colonization to compute the solutions of global... Sample PDF
Artificial Life Optimization Algorithm and Applications
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Chapter 21
Martin Macaš, Lenka Lhotská
A novel binary optimization technique is introduced called Social Impact Theory based Optimizer (SITO), which is based on social psychology model of... Sample PDF
Optimizing Society: The Social Impact Theory Based Optimizer
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Chapter 22
James F. Peters, Shabnam Shahfar
The problem considered in this chapter is how to use the observed behavior of organisms as a basis for machine learning. The proposed approach for... Sample PDF
Ethology-Based Approximate Adaptive Learning: A Near Set Approach
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Chapter 23
Dingju Zhu
Parallel computing is more and more important for science and engineering, but it is not used so widely as serial computing. People are used to... Sample PDF
Nature Inspired Parallel Computing
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Chapter 24
Tang Mo, Wang Kejun, Zhang Jianmin, Zheng Liying
An understanding of the human brain’s local function has improved in recent years. But the cognition of human brain’s working process as a whole is... Sample PDF
Fuzzy Chaotic Neural Networks
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About the Contributors