Computational Intelligence

Frontmatter

1. An Introduction to Computational Intelligence

Abstract

The chapter provides an introduction to computational intelligence. It begins with a thorough review of the underlying principles of artificial intelligence, and examines the scope of computational intelligence in overcoming the limitations of the traditional AI. The chapter then briefly introduces various tools of computational intelligence such as fuzzy logic, neural network, genetic algorithm, belief network, chaos theory, computational learning theory and artificial life. The synergistic behavior of the above tools on many occasions far exceeds their individual performance. A discussion on the synergistic behavior of neuro-fuzzy, neuro-GA, neuro-belief and fuzzy-belief network models is also included in the chapter. A list of tutorial problems is appended at the end of the chapter to build up students’ ability in handling real world problems.

2. Fuzzy Sets and Relations

Abstract

The chapter provides an introduction to fuzzy sets, fuzzy relations and some elementary fuzzy operators such as t-norm, s-norm, max-min composition and max-product composition operators. The extension principle of fuzzy sets and the concept of projection and cylindrical extension have been outlined in the chapter with examples. A brief introduction to fuzzy linguistic variables and fuzzy hedges is also given at the end of the chapter.

3. Fuzzy Logic and Approximate Reasoning

Abstract

A production system generally embodies a set of rules, called knowledge base, a set of facts called database and an inference engine (interpreter) for interpretation of the database with the help of the knowledge base. In the process of interpretation of the database, the inference engine generates new inferences. The mechanism of generation of inferences is well known as reasoning in the treaties of knowledge based systems. Reasoning in predicate logic is usually performed by three fundamental rules, such as modus ponens, modus tollens and syllogisms. The chapter extends the scope of reasoning in knowledge based systems through generalization of the above three rules by using the logic of fuzzy sets. Various forms of fuzzy reasoning with single and multiple antecedent clauses have been introduced in the chapter and the scope of one such reasoning scheme on a VLSI engine has been examined. The chapter ends with a discussion on the principles of fuzzy abductive reasoning.

4. Fuzzy Logic in Process Control

Abstract

The logic of fuzzy sets and its application in approximate reasoning have already been introduced in the last two chapters. This chapter further extends the scope of approximate reasoning of fuzzy logic in industrial process control systems. Two distinct models of fuzzy control namely Mamdani’s model and Takagi-Sugeno’s model have been discussed in this chapter with numerical illustrations. One important aspect of controller design for smart processes is to ensure stability of the closed loop control system. The chapter provides an introduction to stability analysis for the Takagi-Sugeno model, as it nowadays is widely being used in the design of industrial fuzzy controllers. The principle of defuzzification is introduced with an example. Lastly the chapter ends with a discussion on a case study of fuzzy control of a nuclear reactor.

5. Fuzzy Pattern Recognition

Abstract

Classical models of pattern recognition partition a set of patterns into classes depending on the similarity in features of the patterns. When the distinctive features of the patterns are correctly identified, the classes can easily be distinguished in the feature space. Unfortunately, features in most pattern recognition problems are selected on an ad hoc basis, consequently causing the pattern classes to overlap, thereby leading to an ambiguity in object recognition. This chapter presents a well-known technique for fuzzy pattern recognition, capable of partitioning the patterns by soft boundaries. Thus a pattern may be classified into one or more classes with a certain degree of membership to belong to each class. The algorithm for fuzzy pattern recognition is numerically illustrated, and its application in object recognition from real time video frames is also presented.

6. Fuzzy Databases and Possibilistic Reasoning

Abstract

The chapter provides a possibilistic interpretation of fuzzy relational databases containing imprecise and noisy data. It proposes fuzzy equality relations, and represents fuzzy functional dependency using such relations. It also outlines a novel scheme for testing the lossless join decomposition of fuzzy relational databases. The chapter finally employs the above two concepts in the design of fuzzy relational databases. The concepts outlined in the chapter have been illustrated with many examples.

7. Introduction to Machine Learning Using Neural Nets

Abstract

This chapter provides an introduction to machine learning using artificial neural networks. It reviews biological neural networks, and presents a general framework to construct their mathematical models with a view to study their applications in machine learning. The chapter overviews five different types of machine learning such as supervised learning, unsupervised learning, competitive learning, reinforcement learning and Hebbian learning. Stability and convergence are two fundamental issues in studying machine learning algorithms. The interrelationship between stability of a dynamical learning system and convergence of a learning algorithm is presented in detail in this chapter. Concluding remarks are appended at the end of the chapter.

8. Supervised Neural Learning Algorithms

Abstract

The chapter presents supervised learning algorithms for training feed-forward neural networks. It begins with McCulloch-Pitts model and demonstrates its application in realization of binary logic functions. Rosenblatt’s perceptron learning algorithm designed for the McCulloch-Pitts neuronal model is presented next. Application of the perceptron learning model in both linear and nonlinear classification problems is then introduced. The chapter also covered Widrow-Hoff’s ADALINE model and discussed its application in translation and rotation invariant pattern recognition. The most important aspect of the chapter is the derivation of the classical back-propagation learning algorithm from the principles of gradient descent learning. The chapter ended with discussions on Radial Basis Function neural nets and modular neural nets.

9. Unsupervised Neural Learning Algorithms

Abstract

This chapter provides a thorough review of the classical algorithms on unsupervised neural learning. It begins with a brief introduction to recurrent neural topology and then presents in detail both binary and continuous Hopfield nets, their stability analysis and applications. The chapter also presents a detailed overview to adaptive resonance theory and its application in solving the ’stability plasticity conflict’ problem in classical pattern recognition. Finally, the chapter introduces fuzzy associative memory neural nets and outlines algorithms for pattern classification by the proposed neural nets. Concluding remarks are listed at the end of the chapter.

10. Competitive Learning Using Neural Nets

Abstract

The chapter presented different models of competitive learning using neural networks. The first model is concerned with a two layer competitive learning network having a noise-free input realized with an on-center off-surround configuration. An analysis of the model has been presented in detail. The scope of realization of competition by Hebbian learning and the way-out to handle the limitation of Hebbian learning by Oja’s principle have been discussed in detail. The chapter also introduced principal component analysis and self-organizing feature models and examined their applications in face recognition problem.

11. Neuro-dynamic Programming by Reinforcement Learning

Abstract

The chapter introduces the principles of reinforcement learning that rests on the foundation of the penalty-reward mechanism of our natural learning process. It begins with Q-learning and its variants and discusses the scope of realization of Q-learning on neural networks. Two distinct models of neural topologies have been considered for on-line adaptation of weights in the neural networks, following the dynamics of the Q-learning law. The principles of the Q-learning algorithm have been illustrated with the well-known grid-world problem of mobile robots. The convergence analysis of the Q-learning algorithm is presented, and the scope of extension of the Q-learning algorithm in multi-agent learning systems has been addressed at the end of the chapter.

12. Evolutionary Computing Algorithms

Abstract

The chapter presents a new kind of classical algorithms that emulates the biological evolutionary process in intelligent search, machine learning and optimization problems. After a brief introduction to this algorithm, the chapter provides a detailed discussion on one such algorithm, called Genetic Algorithm. An analysis of Genetic Algorithm by the well-known Schema theorem and Markov Chains is then presented. The latter part of the chapter is devoted to discuss the possible applications of Genetic Algorithm in machine learning, intelligent search and derivative-free optimization problems. The chapter ends with a discussion on the scope of another evolutionary algorithm, popularly known as Genetic Programming.

13. Belief Calculus and Probabilistic Reasoning

Abstract

This chapter provides two different techniques for probabilistic reasoning popularly known as Dempster -Shafer theory and Pearl’s evidential model for belief propagation. The former technique is employed to reduce uncertainty in decisions when the relevant information needed to arrive at the decision is obtained from multiple sources with non-uniform levels of authenticity. The latter technique is an extension of classical Bayesian literature. It inputs both causal and evidential information of an event to determine its belief. Pearls’ belief propagation model, to be presented in the chapter, is applied on a causal tree or a graph where nodes denote events and the directed arcs denote cause-effect relationship between each two events. The model has extensive applications in diagnostic systems, where the probabilistic sensory data is fed at the leaves of the causal tree, and the root causes of system failure, which are denoted by non-terminal nodes in the network, are identified though an algorithm for belief propagation.

14. Reasoning in Expert Systems Using Fuzzy Petri Nets

Abstract

The chapter aims at developing new techniques for uncertainty management in expert systems for two generic class problems using fuzzy Petri net that represents logical connectivity among a set of imprecise propositions. One class of problems addressed in the chapter deals with the computation of fuzzy belief of any proposition from the fuzzy beliefs of a set of independent initiating propositions in a given network. The other class of problems is concerned with the computation of steady state fuzzy beliefs of the propositions embedded in the network, from the initial fuzzy beliefs through a process called belief-revision. During belief-revision, a fuzzy Petri net with cycles may exhibit “limitcycle behavior” of fuzzy beliefs for some propositions in the network. No decisions can be arrived at from a fuzzy Petri net with such behavior. To circumvent this problem, techniques have been developed for the detection and elimination of limitcycles. Further, an algorithm for selecting one evidence from each set of mutually inconsistent evidences, referred to as nonmonotonic reasoning, has also been presented in connection with the problems of belief-revision. Finally the concepts proposed for solving the problems of belief-revision have been applied successfully for tackling imprecision, uncertainty, and nonmonotonicity of evidences in an illustrate expert system for criminal investigation.

15. Fuzzy Models for Face Matching and Mood Detection

Abstract

The chapter aims at designing a new methodology for matching of digital gray images using fuzzy membership-distance products, called moment descriptors. These descriptors are estimated for three common kinds of image attributes namely edge, shade and mixed-range. The existing methods for matching of digital images, which are concerned with the comparison of the positions of directed edges, shades and mixed-range in an image with the same of another image, are often prone to error, due to noise and/or variation in illumination. Fuzzy moment descriptors being less sensitive to noise, makes the matching process invariant to the above stray external disturbances. Further, the normalization and sorting of the moment descriptor vectors keep the matching process invariant to size and rotation of images. The general scheme for image matching presented here has successfully been applied to facial image database for personnel identification. The chapter also explores the scope of template matching and human mood detection from facial images using fuzzy logic

16. Behavioral Synergism of Soft Computing Tools

Abstract

The chapter introduced the synergistic aspects of different computational tools of machine intelligence including the logic of fuzzy sets, artificial neural networks, genetic algorithms and belief networks. Each of these tools has its inherent merits and demerits. However, a judicious mixture of these tools may sometimes improve the performance of the overall system to a great extent. The chapter explores some of the possible applications, where the integral effect of two or more computational models far exceeds their individual effects. A case study indicating the synergism of 2 different neural nets and GA has been undertaken in this chapter to study its application in motion planning of mobile robots.

17. Object Recognition from Gray Images Using Fuzzy ADALINE Neurons

Abstract

The chapter aims at extending the scope of application of Widrow-Hoff’s ADALINE model from binary to gray level (fuzzy) pattern recognition. The condition of stability for the extended ADALINE model has been derived and the algorithm for training the multi-layered feed-forward neural net consisting of ADALINE neurons has been presented. The time required for training the neural net is insignificantly small. The scheme for the recognition of objects from their gray level images, using fuzzy ADALINE model, is translation-, rotation- and size- invariant.

18. Distributed Machine Learning Using Fuzzy Cognitive Maps

Abstract

Mammals perform spatial reasoning by a specialized structure called cognitive maps located in the hippocampus region of their forebrain. In the treaties of computational intelligence, the phrase cognitive maps, however, has a wider meaning. It includes encoding of knowledge about causal events and their automated recall. Modeling of cognitive maps by fuzzy logic is apparent because of the inherent fuzziness of most real world knowledge bases. The chapter provides a thorough overview of various models of cognitive maps and their learning behavior. The dynamics of the learning models have been analyzed to determine the condition for their stability. The chapter ends with a discussion on the scope of application of the proposed models in practical engineering systems.

19. Machine Learning Using Fuzzy Petri Nets

Abstract

The chapter presents a new model for unsupervised learning and reasoning on a special type of cognitive maps, realized with Petri nets. The unsupervised learning process in the present context adapts the weights of the directed arcs from transition to places in the Petri net. A Hebbian type learning algorithm with a natural decay in weights is employed here to study the dynamic behavior of the algorithm. The algorithm is conditionally stable for a suitable range of the mortality rate. A pre-trained network with stable weights may be used in reasoning phase for computing beliefs of the desired propositions from the supplied beliefs of the axioms (places with no input arcs). Because of the conditional stability of the learning algorithm, it may be employed in complex decision-making and learning such as automated car driving in an accident-prone environment. The chapter also presented a new scheme for knowledge refinement by adaptation of weights in a fuzzy Petri net using a different form of Hebbian learning.

20. Computational Intelligence in Tele-Communication Networks

Abstract

The chapter discusses the scope of computational models of machine intelligence in tele-communication networks. It begins with a brief introduction to computer networks, and outlines two popular reference models of network architecture. The chapter then presents three interesting problems that the design engineers face in the network layer of the reference models. The problems are centered around network routing, congestion control and call admission control. Classical control and optimization techniques are not suitable for real time solution to these problems. Thus a computational intelligence approach to solve the problems in real time is proposed. In this chapter, routing, congestion control and call admission control have been taken care of by genetic algorithm, fuzzy logic and artificial neural networks respectively.

21. Computational Intelligence in Mobile Robotics

Abstract

The chapter deals with mobile robots and its engineering applications. It begins with a brief introduction to the anatomy of mobile robots, and explores the scope of intelligent models in building automation for the robots. The chapter includes a comparative study of different neural topologies in path-planning application of the robots. It also outlines image segmentation and localization of a moving target in connection with the discussion on target-tracking application of the robots. The scope of extended Kalman filter in the proposed application has also been studied in detail.

22. Emerging Areas of Computational Intelligence

Abstract

The chapter provides an introduction to the new members of the computational intelligence family that are currently gaining importance for their increasing applications in both science and engineering. The list of the new members includes Artificial Life, Particle Swarms, Artificial Immune Systems, Chaos Theory, Rough Set Theory and Granular Computing. The biological concepts involved in the first three topics are briefly explained to enable the readers to construct their mathematical models for specific engineering applications. The chaos theory is introduced to demonstrate the behavior of fuzzy dynamical systems. The chaotic behavior of fuzzy dynamics is illustrated with typical models of fuzzy liars. Rough sets and granular computing are presented in a nutshell to familiarize the readers with these growing disciplines of knowledge.

23. Research Problems for Graduate Thesis and Pre-Ph D Preparatory Courses

Abstract

This chapter addresses selected research problems in computational intelligence. The problems are introduced informally so that anyone without any background in the specific domain easily understands them. The problems require either a mathematical formulation or a computer simulation for their solutions. An outline to the solution of the problems is also suggested.

Backmatter