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LEARNING FUZZY LOGIC from EXAMPLES 8'' 8'' M LEARNING FUZZY LOGIC FROM EXAMPLES 8'' 8'' m- A Thesis Presented to The Faculty of the College of Engineering and Technology Ohio University In Partial Fulfillment of the Requirements for the Degree Master of Science Luis Alfonso Quiroga -Aranibay March 1994 ACKNOWLEDGMENTS I would like to first thanks my advisor, Dr. Luis C. Rabelo, for his continuos commitment to quality and his tireless contributions for a better Industrial and Systems Engineering Department at Ohio University. His encouragement during my initial "fuzzy" days was fundamental in the development of this work. I dedicate this work to my parents, because all that I am I owe it to them. Their infinite love and understanding for their children will forever be the guidelines in my life. I also dedicate this work to my sister and my brothers whose constant care and affection always give me the perseverance to try my best. Special thanks to Dr. Donald D. Scheck for being the person who introduced me to the world of Fuzzy Logic. I appreciate very much his interest on my experiences in the manufacturing environment and my research. I owe special gratitude to Dr. James J. Fales and Mr. Roger S. Vincent. They have been the most influential people in my years at Ohio University. Their willingness to share their knowledge and professional experience has granted me with the invaluable opportunity to perceive the demands of the professional world early on in my career. I am indebted for their trust in my assignments at the Center for Automatic Identification. My friend and teacher, Dr. Evgueni Mourzine, deserves my recognition for his teachings in C++. His input and suggestions were always helpful and insightful. My deepest appreciation to Mrs. Linda Stroh, Mrs. Brenda Stover, and Mrs. Polly Sandenburgh. Their kind friendship and words of encouragement were essential for the completion of this work. My endless gratitude to Monica, Connie, Tonga, Kevin, Franklin, Gaspar, and Makoto: they accompanied me during the writing of this thesis and they are the foundation in which it rests. You made the good times better and the tough times easier: the last few years worth living for. My love to all of you. TABLE OF CONTENTS ... ACKNOWLEDGMENTS ........................................................................................... m TABLE OF CONTENTS .... ... .. .. .. , . iv LIST OF TABLES .................................................................................................... vi LIST OF FIGURES ................................................................................................... vii Chapter I Introduction .. 1 Chapter I1 Literature Review 2.1 Fuzzy Logic: Basic Concepts ......................................................................5 2.2 Fuzzy Logic Control: Current Application ................................................15 2.3 Approaches to Manufacturing Planning ....................................................22 2.3.1 Traditional Techniques Mathematical Programming and Analytical Models.. .. .. .. .. .... ... ... ... .. ... .. 22 Dispatching Rules ................................................................................24 2.3.2 Artificial Intelligence Techniques Knowledge-Based Expert Systems.................................................... 26 Artificial Neural Networks Application . ............. .... .... .... .. ...... ...... 28 Chapter I11 The Wang and Mendel Methodology 3.1 Fuzzy Associative Memory .......................................................................29 3.2 Generating Fuzzy Rules from Numerical Data Divide Input and Output Spaces into Fuzzy Region .............................31 Generate Fuzzy Rules from the Given Data Pairs ................................. 33 Assign a Degree to Each Rule ..............................................................34 Create a Combined FAM Bank ............................................................35 Determine a Mapping based on the FAM Bank ....................................36 Chapter IV Application of the Wang-Mendel Methodology in Robot Motion Control 4.1 Robot Motion Control Case Study ........ .. .. ....... ... .. .. .. .. .. 38 4.2 Development of the Fuzzy Logic Controller ...............................................45 4.3 The Fuzzy Machine ..... .. .. .. .. ...... ....... ... ......... .. ......... 49 4.4 Testing of the Fuzzy Logic Controller ........................................................57 v Chapter V Application of the Wang-Mendel Methodology in Job-Shop Scheduling 5.1 Job-Shop Scheduling: Introduction ............................................................65 5.2 Job-Shop Scheduling Case Study ...............................................................67 5.2.1 Training the Fuzzy Logic Controller ........................................71 5.2.2 Job-Shop Scheduling: Fuzzy ...........................................................75 5.3 Neural Networks Approach .......................................................................79 5.4 Quinlan's ID3 Machine Learning Approach ................................................83 Chapter VI Conclusions .......................................................................................................90 Further Research ...............................................................................................93 Selected References .................................................................................................... 95 Appendix A "Learning from Examples" Methods 1. Artificial Neural Networks ...........................................................102 2. Machine Learning ........................................................................106 Appendix B Sample Data Sets for the Robot Motion Control Case Study ............... 111 Appendix C Degree of Membership Functions for Robot Motion Control ............... 114 Appendix D Sample of Initial Fuzzy Rules for Robot Motion Control ..................... 118 Appendix E 1I 1 Control Fuzzy Rules for Robot Motion Control ............................ 121 Appendix F Training and Testing Data Pair Samples for Job-Shop Scheduling ........ 134 Appendix G 15 Control Fuzzy Rules for Job-Shop Scheduling ................................ 137 Appendix H Program Source Code ......................................................................... 140 LIST OF TABLES Table 1: Fuzzy Ranges for Inputs and Outputs: Robot Motion Control ...................... 47 Table 2: Degree of Membership Functions: Robot Motion Control ............................ 51 Table 3: Results for Testing Data: Robot Motion Control ..........................................64 Table 4: Fuzzy Ranges for Inputs and Outputs: Job-Shop Scheduling ........................ 69 Table 5: Degree of Membership Functions: Job-Shop Scheduling ..............................73 Table 6: Results for Testing Data: Job-Shop Scheduling ............................................78 Table 7: Mismatched Data Sets: Job-Shop Scheduling ...............................................79 Table 8: History File Report for the Neural Networks Approach ................................81 Table 9: ID3 Leaf Intervals: Job-Shop Scheduling ..................................................... 88 Table 10: ID3 Results: Job-Shop Scheduling .............................................................89 Table 11 : Comparison Criteria for "Learning from Examples" Techniques .................92 vii LIST OF FIGURES Figure Page 2.1 Definition of a Membership Function ..................................................................7 2.2 Linguistic Variables and the Effects of Fuzzy Modifiers ......................................9 2.3 Components of a Fuzzy Logic Controller ..........................................................12 2.4 Fuzzification .....................................................................................................13 2.5 Centroid Method ..............................................................................................14 2.6 Fuzzy Sets for the Mamdani-Assilian Steam Engine .......................................... 16 2.7 Fuzzy Mapping for the Mamdani-Assilian Steam Engine ................................... 17 3.1 Division of Input and Output Spaces into Fuzzy Regions .................................. 32 3.2 FAM Bank Representation ................................................................................36 4.1 Two Dimensional 2 Degree of Freedom Manipulator ........................................ 40 4.2 Final Configuration at point (x,y) for the Robot Arm .........................................42 4.3 Joint Angle Solution .........................................................................................43 4.4 Configuration for the Robot Motion Control Case Study ..................................44 4.5 Degree of Membership Functions for Robot Motion Control .............................48 4.6 Definition of the Degree of Membership Functions ............................................50 4.7 Degree of Membership Values for Numerical Example ......................................53 4.8 Definition of a FAM Bank ................................................................................ 56 4.9 FAM Bank for the Robot Motion Control Case Study ......................................58 4.10 Fuzzy Logic Controller Response to Testing Data ............................................. 60 5.1 The Job-Shop Scheduling Operation .................................................................. 65 5.2 Typical Schedule for the Job-Shop
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