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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. © 2010 Intech Free online edition of this book you can find under www.sciyo.com Additional copies can be obtained from: publication@sciyo.com 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 Preface V 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 Lyapunov Function 041 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 5. Adaptive Neuro-Fuzzy Systems 085 Azar, Ahmad Taher 6. A Hybrid Fuzzy System for Real-Time Machinery Health Condition Monitoring 111 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 [...]... 0 .1 1 0.7 0.2 0.7 0 0.9 0.3 1 0.3 0.2 0 .1 0 0 .1 0.9 1 0.2 0 .1 0 1 1 0.3 0.4 0 .1 1 1 0.6 1 0.8 0.23 0.22 0.42 0.92 0. 51 0.6 0.8 0.3 0.8 0.2 0.04 0. 81 0. 91 0.9 0.97 0.4 0 0 .1 0.7 0.8 0.24 ⎤ 0.53 ⎥ ⎥ 0.74 ⎥ , ⎥ 0.25 ⎥ 0. 61 ⎥ ⎦ 0.9 ⎤ 0.3 ⎥ ⎥ 0.4 ⎥ , ⎥ 0.5 ⎥ 0.2 ⎥ ⎦ GT = [ 10 15 20 25 30 ] Here, GT denotes the transpose of G Total score for each individual student is then obtained by formula (1) as s1 s2... of question 1 The surface view of the relation of the rule base in Table 1a is shown in Fig 5 Fig 5 Surface view of rule base in Table 1a for the difficulty (left) and rule base in Table 1b for the cost (right) 10 Fuzzy Systems (a) Difficulty Time rate Accuracy 1 2 3 4 5 1 3 4 4 5 5 2 2 3 4 4 5 3 2 2 3 4 4 4 1 2 2 3 4 5 1 1 2 2 3 (b) Cost Complexity Difficulty 1 2 3 4 5 1 1 1 2 2 3 2 1 2 2 3 4 3 2... order Example Assume that 10 students laid to an exam of 5 questions and the accuracy rate matrix, the time rate matrix, and the grade vector are given as follows (Bai & Chen, 2008b; Saleh & Kim, 2009): ⎡ 0.59 ⎢ ⎢ 0. 01 A = ⎢0.77 ⎢ ⎢ 0.73 ⎢ 0.93 ⎣ 0.35 0.27 0.69 0.72 0.49 ⎡0.7 ⎢ 1 ⎢ T=⎢ 0 ⎢ ⎢0.2 ⎢ 0 ⎣ 1 0 .14 0.97 0 .18 0.08 0.66 0.04 0. 71 0 .16 0. 81 0 .11 0.88 0 .17 0.5 0.65 0.08 0 .16 0.86 0.02 0.93 0.84 0.04... 0.45 0. 31 0. 711 0.47 0.637 ] , T T = [ 0.57 0.48 0. 31 0.50 0.57 ] Based on the fuzzy MFs in Fig 3 we obtain the fuzzy accuracy rate matrix and the fuzzy time rate matrix as: Fuzzy Systems in Education: A More Reliable System for Student Evaluation 7 0 0 ⎤ ⎡0 0.25 0.75 ⎢0 0.95 0.05 0 0 ⎥ ⎢ ⎥ 0 0 0.945 0.055 ⎥ , FA = ⎢0 ⎢ ⎥ 0 0 ⎥ ⎢0 0 .15 0.85 ⎢0 0 0. 315 0.685 0 ⎥ ⎣ ⎦ 0 0.65 0.35 0 ⎤ ⎡0 ⎢0 0 .1 0.9 0 0⎥... computation uses the Mamdani’s fuzzy interference mechanism and is obtained by formula (7) as the following: α 14 = = m ax {( l1 , l2 ) ℜ ( l1 , l2 ) = 4} { m in ( fa 1, l1 , ft 1, l2 max {( 1, 2 ) , ( 1, 3 ) , ( 2 ,3 ) , ( 2 ,4 ) , ( 3 ,4 ) , ( 3 ,5 ) , ( 4 ,5 )} )} { min ( fa 1, l1 , ft 1, l2 )} = m ax {min ( 0 , 0 ) , min ( 0 , 0.65 ) , min ( 0.25, 0.65 ) , min ( 0.25, 0.35 ) , min ( 0.75, 0.35 )... Co = [coik], m x 1, where coik ∈ [0, 1] denotes the degree of complexity of question i belonging to the complexity level k Example For the above example we get the following, in fuzzy domain, by the domain expert: 0 0 0 1 ⎤ ⎡0 ⎢0 0.33 0.67 0 0 ⎥ ⎢ ⎥ 0 0 0 .15 0.85 ⎥ P = ⎢0 ⎢ ⎥ 0 0 0 0 ⎥ 1 ⎢0 0.07 0.93 0 0 ⎥ ⎣ ⎦ 6 Fuzzy Systems 0.85 0 .15 0 0 ⎤ ⎡ 0 ⎢ 0 0 0.33 0.67 0 ⎥ ⎢ ⎥ 0 0 0.69 0. 31 Co = ⎢ 0 ⎢ ⎥ 0... 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 (20 01) pointed out that the system for students’ 2 Fuzzy Systems achievement evaluation should consider... (c) Adjustment Cost Importance 1 2 3 4 5 1 1 1 2 2 3 2 1 2 2 3 4 3 2 2 3 4 4 4 2 3 4 4 5 5 3 4 4 5 5 1: “Low”, 2: “more or less low”, 3: “medium”, 4: “more or less high” and 5: “high” Table 1 A fuzzy rule base to infer the difficulty, cost, and adjustment At the next cost node, in Step 1, the crisp values of D obtained at the previous node are fuzzified to obtain the fuzzy difficulty matrix as: 0 0.622... introduction in 19 65 by Lotfi Zadeh (19 65), the fuzzy set theory has been widely used in solving problems in various fields, and recently in educational evaluation Biswas (19 95) 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 (19 99) presented two methods for applying fuzzy. .. also given a grade vector, G, of dimension m x 1 G = [gi], m x 1, where gi ∈ [1, 10 0] denotes the assigned maximum score of question i satisfying m ∑ g = 10 0 i i =1 Based on the accuracy rate matrix, A, and the grade vector G, we obtain the total score vector of dimension n x 1, S = ATG = [sj], n x 1, (1) where sj ∈ [0, 10 0] is the total score of student j The “classical” ranks of students are then . 0. 81 0.65 0.93 0.39 0. 51 0.97 0. 61 A ⎡ ⎢ = ⎣ , ⎤ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎦ 0.7 0.4 0 .1 1 0.7 0.2 0.7 0.6 0.4 0.9 1 0 0.9 0.3 1 0.3 0.2 0.8 0 0.3 0 0 .1 0 0 .1 0.9 1 0.2 0.3 0 .1 0.4 , 0.2 0 .1 0 1 1. 2009): 0.59 0.35 1 0.66 0 .11 0.08 0.84 0.23 0.04 0.24 0. 01 0.27 0 .14 0.04 0.88 0 .16 0.04 0.22 0. 81 0.53 0.77 0.69 0.97 0. 71 0 .17 0.86 0.87 0.42 0. 91 0.74 0.73 0.72 0 .18 0 .16 0.5 0.02 0.32 0.92. Fuzzy Systems 10 (a) Difficulty Time rate Accuracy 1 2 3 4 5 1 3 4 4 5 5 2 2 3 4 4 5 3 2 2 3 4 4 4 1 2 2 3 4 5 1 1 2 2 3 (b) Cost Complexity Difficulty 1 2 3 4 5 1 1 1