Fuzzy Systems Part 1 doc

The application of the fuzzy sets involves different technologies, such as fuzzy clustering on image processing, classification, identification and fault detection, fuzzy controllers to

Fuzzy Systems

Fuzzy Systems

Edited by Ahmad Taher Azar

Intech

IV

Published by Intech

Intech

Olajnica 19/2, 32000 Vukovar, Croatia

Abstracting and non-profit use of the material is permitted with credit to the source Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher No responsibility is accepted for the accuracy of information contained in the published articles Publisher assumes no responsibility liability for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained inside After this work has been published by the Intech, authors have the right to republish it, in whole or part, in any publication of which they are an author or editor, and the make other personal use of the work

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First published February 2010

Printed in India

Technical Editor: Teodora Smiljanic

Cover designed by Dino Smrekar

Fuzzy Systems, Edited by Ahmad Taher Azar

p cm

ISBN 978-953-7619-92-3

Preface

Since the idea of the fuzzy set was proposed in 1965, many developments have occurred in this area Applications have been made in such diverse areas as medicine, engineering, management, behavioral science, just to mention some The application of the fuzzy sets involves different technologies, such as fuzzy clustering on image processing, classification, identification and fault detection, fuzzy controllers to map expert knowledge into control systems, fuzzy modeling combining expert knowledge, fuzzy optimization to solve design problems Fuzzy systems are used in the area of artificial intelligence as a way

to represent knowledge This representation belongs to the paradigm of behavioral representation in opposition to the structural representation (neural networks) The foundation of this paradigm is that intelligent behavior can be obtained by the use of structures that not necessarily resemble the human brain A very interesting characteristic of the fuzzy systems is their capability to handle in the same framework numeric and linguistic information This characteristic made these systems very useful to handle expert control tasks While several books are available today that address the mathematical and philosophical foundations of fuzzy logic, none, unfortunately, provides the practicing knowledge engineer, system analyst, and project manager with specific, practical information about fuzzy system modeling Those few books that include applications and case studies concentrate almost exclusively on engineering problems: pendulum balancing, truck backeruppers, cement kilns, antilock braking systems, image pattern recognition, and digital signal processing Yet the application of fuzzy logic to engineering problems represents only a fraction of its real potential As a method of encoding and using human knowledge in a form that is very close to the way experts think about difficult, complex problems, fuzzy systems provide the facilities necessary to break through the computational bottlenecks associated with traditional decision support and expert systems Additionally, fuzzy systems provide a rich and robust method of building systems that include multiple conflicting, cooperating, and collaborating experts (a capability that generally eludes not only symbolic expert system users but analysts that have turned to such related technologies

as neural networks and genetic algorithms) Yet the application of fuzzy logic in the areas of decision support, medical systems, database analysis and mining has been largely ignored

by both the commercial vendors of decision support products and the knowledge engineers that use them

VI

This book is intended to present fuzzy logic systems and useful applications with a self-contained, simple, readable approach It is intended for the intelligent reader with an alert mind The approach, the organization, and the presentation of this book are also hoped to enhance the accessibility to existing knowledge beyond its contents The book is divided into twelve chapters In Chapter 1 Gaussian membership functions (MFs) are proposed as an alternative to the traditional triangular MFs in order to improve the reliability and robustness of the system Gaussian MFs provide smooth transition between levels and provides a way to fire the maximum number of rules in the rule base and hence a more accurate representation of the input-output relationship is achieved Chapter 2 describes robust H∞ control problems for uncertain Takagi-Sugeno (T-S) fuzzy systems with immeasurable premise variables A continuous-time Takagi-Sugeno fuzzy system is first considered The same control problems for discrete-time counterpart are also considered Chapter 3 deals with the control of T-S fuzzy systems using fuzzy weighting-dependent lyapunov function In Chapter 4, the digital fuzzy control system considering a time delay is developed and its stability analysis and design method are proposed The discrete Takagi- Sugeno(TS) fuzzy model and parallel distributed compensation(PDC) conception for the controller are used The proposed control system can be designed using the conventional methods for stabilizing the discrete time fuzzy systems and the feedback gains of the controller can be obtained using the concept of the linear matrix inequality (LMI) feasibility problem

Chapter 5 presents an overview of adaptive neuro-fuzzy systems developed by exploiting the similarities between fuzzy systems and certain forms of neural networks, which fall in the class of generalized local methods The chapter starts by making a classification of the different types of neuro-fuzzy systems and then explains the modeling methodology of neuro-fuzzy systems Finally, the chapter is completed by a practical case-study Chapter 6 describes a hybrid fuzzy system to develop a new technique, an integrated classifier, for real-time condition monitoring in, especially, gear transmission systems In this novel classifier, the monitoring reliability is enhanced by integrating the information of the object’s future states forecast by a multiple-step predictor; furthermore, the diagnostic scheme is adaptively trained by a novel recursive hybrid algorithm to improve its convergence and adaptive capability Chapter 7 presents the mathematical theory of fuzzy filtering and its applications in life science Chapter 8 is devoted to develop applications to enable information extraction under uncertainty, particularly on the conception and design

of autonomous systems for natural language processing applications specifically on question and answering systems and textual entailment mechanism

Chapter 9 deals with the algorithms of the body signature identification The developed systems can be used to detect body position on the bed as well as the type of body movement Using the body movement, the time period between two successive movement and the sensor amplitude, one can identify the sleep type (normal, agitate, abnormal, convulsive, etc) The system can be adapted to the person and does not depend on their weight, size or position Chapter 10 is devoted to the probelm of students’ evaluation method This chapter proposes the use of the fuzzy set technique that will be applied in the evaluation process of the industrial automation systems learning area, aiming to lessen the evaluation complexity and ambiguity in this area It is also important to emphasize that this fuzzy learning evaluation methodology may be used when training industrial plant operators and engineers who have already been working in the area but must be trained in

VII

new, emerging technologies Chapter 11 studies the combination of particle swarm optimization (PSO) and ant colony optimization (ACO) for the design of fuzzy systems One problem of PSO in FS design is that its performance is affected by initial particle positions, which are usually randomly generated in a continuous search space A poor initialization usually results in poor performance Searching in the discrete-space domain by ACO helps

to find good solutions However, the search constraint in a discrete-space domain restricts learning accuracy The motivation on the combination of ACO and PSO is to compensate the aforementioned weakness of each method in FS design problems Finally, Chapter 12 presents a directed formation control problem of heterogeneous multi-agent systems Fuzzy logical controller for multi-agent systems with leader-following is presented, which can not only accomplish the desired triangle formation but also ensure that the followers’ speeds converge to the leader’s velocity without collision during the motion The proposed Fuzzy logical controller is interesting for the design of optimization algorithms that can ensure the triangle formation that multi-agent systems are required maintaining a nominated distance The book is written at a level suitable for use in a graduate course on applications of fuzzy systems in decision support, nonlinear modeling and control The book discusses novel ideas and provides a new insight into the studied topics For this reason, the book is a valuable source for researchers in the areas of artificial intelligence, data mining, modeling and control The realistic examples also provide a good opportunity to people in industry to evaluate these new technologies, which have been applied with success

This text is addressed to engineering lecturers, researchers extending the frontiers of knowledge, professional engineers and designers and also students A hallmark of fuzzy logic methods is that the cultural gap between researchers and practitioners is not apparent, the linguistic formulation of problems and conclusions is equally coherent to both

I would like to acknowledge the invaluable help given by Aleksandar Lazinica in the final stages of compiling the text Any flaws that remain are mine Comments on any aspects

of the text would be welcome

Editor

Ahmad Taher Azar, PhD

Electrical Communication & Electronics Systems Engineering department,

Modern Science and Arts University (MSA),

6th of October City,

Egypt

Contents

1 Fuzzy Systems in Education:

A More Reliable System for Student Evaluation 001

Ibrahim A Hameed and Claus G Sorensen

2 Control Design of Fuzzy Systems with Immeasurable Premise Variables 017

Jun Yoneyama and Tomoaki Ishihara

3 Control of T-S Fuzzy Systems Using Fuzzy Weighting-Dependent

Sung Hyun Kim and PooGyeon Park

4 Digital Stabilization of Fuzzy Systems with Time-Delay

and Its Application to Backing up Control of a Truck-Trailer 069

Chang-Woo Park

Azar, Ahmad Taher

6 A Hybrid Fuzzy System for Real-Time Machinery

Wilson Wang

7 Fuzzy Filtering: A Mathematical Theory and Applications in Life Science 129

Mohit Kumar, Kerstin Thurow, Norbert Stoll, and Regina Stoll

8 Information Extraction from Text – Dealing with Imprecise Data 147

Turksen, I.Burhan and Celikyilmaz, Asli

X

9 The Algorithms of the Body Signature Identification 169

Hnatiuc Mihaela

10 Students’ Evaluation based on Fuzzy Sets Theory 185

Eduardo André Mossin, Rodrigo Palucci Pantoni and Dennis Brandão

11 Combination of Particle Swarm and Ant Colony Optimization

Algorithms for Fuzzy Systems Design 195

Chia-Feng Juang

12 Triangle Formation of Multi-Agent Systems

with Leader-Following on Fuzzy Control 209

Hongyong Yang and Jianzhong Gu

1

Fuzzy Systems in Education: A More Reliable

System for Student Evaluation

Ibrahim A Hameed and Claus G Sorensen

Aarhus University, Research Centre Foulum

Blichers Allé 20, DK-8830, Tjele,

Denmark

1 Introduction

Student evaluation is the process of determining the performance levels of individual students in relation to educational learning objectives A high quality evaluation system certifies, supports, and improves individual achievement and ensures that all students receive a fair evaluation in order not to constrain students' present and future prospects Thus, the system should regularly be reviewed and improved to ensure that it is suitable, fair, impartial and beneficial to all students It is also desirable that the system is transparent and automation measures should be embedded in the evaluation Fuzzy reasoning has proven beneficial to infer scores of students (e.g Saleh & Kim, 2009) However, in order to improve the reliability and robustness of the system, Gaussian membership functions (MFs) are proposed as an alternative to the traditional triangular MFs

Since its introduction in 1965 by Lotfi Zadeh (1965), the fuzzy set theory has been widely used in solving problems in various fields, and recently in educational evaluation Biswas (1995) presented two methods for evaluating students’ answer scripts using fuzzy sets and a matching function; a fuzzy evaluation method and a generalized fuzzy evaluation method Chen and Lee (1999) presented two methods for applying fuzzy sets to overcome the problem of rewarding two different fuzzy marks the same total score which could result from Biswas’ method (1995) Echauz and Vachtsevanos (1995) proposed a fuzzy logic system for translating traditional scores into letter-grades Law (1996) built a fuzzy structure model for an educational grading system with its algorithm aimed at aggregating different test scores in order to produce a single score for an individual student He also proposed a method to build the MFs of several linguistic values with different weights Wilson, Karr and Freeman (1998) presented an automatic grading system based on fuzzy rules and genetic algorithms Ma and Zhou (2000) proposed a fuzzy set approach to assess the outcomes of Student-centered learning using the evaluation of their peers and lecturer Wang and Chen (2008) presented a method for evaluating students’ answer scripts using fuzzy numbers associated with degrees of confidence of the evaluator From the previous studies, it can be found that fuzzy numbers, fuzzy sets, fuzzy rules, and fuzzy logic systems are and have been used for various educational grading systems

Evaluation strategies based on fuzzy sets require a careful consideration of the factors included in the evaluation Weon and Kim (2001) pointed out that the system for students’

Fuzzy Systems

2

achievement evaluation should consider three important factors of the questions which the

students answer: the difficulty, the importance, and the complexity Singleton functions

were used to describe the factors of each question reflecting the effect of the three factors

individually, but not collectively Bai and Chen (2008b) stressed that the difficulty factor is a

very subjective parameter and may cause an argument about fairness in the evaluation

The automatic construction of the grade MFs of fuzzy rules for evaluating student’s learning

achievement has been attempted (Bai & Chen, 2008a) Also, Bai and Chen (2008b) proposed

a method for applying fuzzy MFs and fuzzy rules for the same purpose To solve the

subjectivity of the difficulty factor embedded in the method of Weon and Kim (2001), Bai

and Chen (2008b) acquired the difficulty parameter as a function of accuracy of the student’s

answer script and time used for each question However, their method still has the

subjectivity problem, since the resulting scores and rankings are heavily dependent on the

values of several weights which are assessed by the subjective knowledge of domain

experts

Saleh and Kim (2009) proposed a three node fuzzy logic approach based on Mamdani’s

fuzzy inference engine and the centre-of-gravity (COG) defuzzification technique as an

alternative to Bai and Chen’s method (2008b) The transparency and objective nature of the

fuzzy system makes their method easy to understand and enables teachers to explain the

results of the evaluation to sceptic students The method involved conventional triangular

MFs of fixed parameters which could result in different results when changed In this

chapter, the Gaussian MFs are proposed as an alternative and a sensitivity study is

conducted to get the appropriate values of their parameters for a more robust evaluation

system

The chapter will be organized as follows: In Section 2, a review of the three nodes fuzzy

evaluation method based on triangular MFs is introduced In Section 3, Gaussian MFs are

proposed for a more robust evaluation system A comparison of the two methods is

presented in Section 4 Conclusions are drawn in Section 5

2 A review of the three nodes fuzzy evaluation system

The method proposed by Bai and Chen (2008b) has several empirical weights which are

determined subjectively by the domain expert Quite different ranks can be obtained

depending on these weight values By using this method, the examiners could not easily

verify how new ranks are acquired and could not persuade sceptical students Naturally,

there is no method to determine the optimum values of these weights Also, the weighted

arithmetic mean formula used to compute the outputs do not satisfy the concept of fuzzy

set To reduce the degree of subjectivity in this method and provide a method based on the

theory of fuzzy set, Saleh and Kim (2009) proposed a system applying the most commonly

used Mamdani’s fuzzy inference mechanism (Mamdani, 1974) and center of gravity (COG)

defuzzification technique In this way, the system is represented as a block diagram of fuzzy

logic nodes as shown in Fig 1 The model of Bai and Chen (2008b) can be considered as a

simple specific case of the block diagram by replacing each node with a weighted arithmetic

mean formula The system consists of three nodes; the difficulty node, the cost node and the

adjustment node Each node of the system behaves like a fuzzy logic controller (FLC in Fig

1) with two scalable inputs and one output, as in Fig 2 Each FLC maps a two-to-one fuzzy

relation by inference through a given rule base