This book has grown out of the lectures that author delivered over the years on the subject to undergraduate and postgraduate students of engineering.
AN INTRODUCTION TO FUZZY SET THEORY AND FUZZY LOGIC
by
C. Mohan
Dedicated to the sweet memory of dear parents: Shri Krishan Gopal and Smt.Vidya Wanti. Their memory lingers. Chander Mohan
Acknowledgements This book has grown out of the lectures that author delivered over the years on the subject to undergraduate and postgraduate students of engineering and mathematics at Roorkee University (now IIT Roorkee), as well as his interaction and discussions on the subject with his colleagues and research scholars. The author would like to place on record his deep appreciation of their contribution in making him develop the understanding of the subject the way it is being presented in this book. While writing a text book of this nature, it is but natural to draw upon the available literature on the subject. Author expresses his sincere gratitude to all the authors and publishers whose works he has utilized in the write up of this book. Most of the work related to the preparation of manuscript of this book has been carried out by the author while working as a Professor in Computer Science at Ambala College of Engineering and Applied Research, Devasthali, Ambala (Haryana). Necessary facilities provided by the Management of the Institute for this purpose are also gratefully acknowledged. I shall be failing in my duty if I do not place on record the moral support provided by my wife Smt. Tripta Kumari who has been a source of strength and has always stood by me through thick and thin.
Ambala April 2010
Chader Mohan (C. Mohan)
Preface Fuzzy sets and Fuzzy Logic is a fast developing field of study and research. It has practical real life applications. Several books on the subject such as ‘Fuzzy Set Theory and its Applications’ by Zimmermann and ‘Fuzzy Set and Fuzzy Logic’ by George J. Klir and Bo Yuann are now available. However most of the books currently available are written by engineers and scientists who while writing these books had generally in mind a specialised set of readers who are primarily interested in the application of fuzzy set theory in some particular field. The subject has now come of age and is fit to be studied for its own sake like other subjects of basic mathematics such as set theory, algebra and calculus. In fact the subject is now being included in the undergraduate and postgraduate curricula of study in several disciplines of study including mathematics. The book has been written with a general type of reader in mind who wants to study the subject for its own sake or is interested in applying to solve problems in his own field of interest. The book presents the basic rudiments of fuzzy set theory and fuzzy logic in a manner in which other basic topics of mathematics such as ‘set theory’, ‘algebra’ and ‘calculus’ etc. are normally presented. No specialised knowledge of any engineering or other discipline is expected from the reader. It is written from a beginners point of view. A student belonging to any discipline and having mathematics background of 10 + 2 level should find no difficulty in understanding the topics presented in the book. Effort has been made to tread middle path which avoids the extremes of abstract mathematical proofs as well as the knowledge of specialised technical details of the areas of application. The author had the privilege of teaching this subject to the undergraduate and postgraduate engineering and mathematics students for a number of years at Roorkee University (now IIT Roorkee). He also used it in his research work related to the development of computational algorithms for solving real life optimization problems. The book is intended to enable the reader to get a clear insight into the basic concepts of the subject. A special feature of the book is that at the end of each chapter the set of exercises is preceded by a set of short answer review type questions. These are intended to help the reader in checking that he/she has correctly grasped the basic concepts developed in the text of the chapter before he/she embarks upon solving the exercises that follow. Answers to (i)
most of these review questions are of yes or no type. However, these are not explicitly provided. These are available in the main text of the chapter. A reader in doubt about the correctness of his/her answer may refer back to the relevant portion in the main text of the chapter. The book can be used as a textbook for the study of the topics of fuzzy set theory, fuzzy logic and their applications both at the undergraduate and postgraduate level in mathematics and other disciplines of science, arts, engineering and medicine. It is not necessary that all the topics presented in the book be read or taught. A judicious choice of the course content can be framed keeping in view the background and requirements of the students to whom it is to be taught. The book can also be used as a reference book for those interested in making use of fuzzy set theory and fuzzy logic in their fields of study and work. Author would welcome such comments and suggestions from the students, teachers and other users of this book which may help him in its further improvement.
