Fuzzy Logic And Probability Applications

Probabilists and fuzzy enthusiasts tend to disagree about which philosophy is best and they rarely work together. As a result, textbooks usually suggest only one of these methods for problem solving, but not both. This book is an exception. The authors, investigators from both fields, have combined their talents to provide a practical guide showing that both fuzzy logic and probability have their place in the world of problem solving. They work together with mutual benefit for both disciplines, providing scientists and engineers with examples of and insight into the best tool for solving problems involving uncertainty. Fuzzy Logic and Probability Applications: Bridging the Gap makes an honest effort to show both the shortcomings and benefits of each technique, and even demonstrates useful combinations of the two. It provides clear descriptions of both fuzzy logic and probability, as well as the theoretical background, examples, and applications from both fields, making it a useful hands-on workbook for members of both camps. It contains enough theory and references to fundamental work to provide firm ground for both engineers and scientists at the undergraduate level and above. Readers should have a familiarity with mathematics through calculus.

Shows both the shortcomings and benefits of each technique, and even demonstrates useful combinations of the two.

FUZZY LOGIC APPLICATIONS IN COMPUTER SCIENCE AND MATHEMATICSTICS The prime objective of developing this book is to provide meticulous details about the basic and advanced concepts of fuzzy logic and its all-around applications to different fields of mathematics and engineering. The basic steps of fuzzy inference systems starting from the core foundation of the fuzzy concepts are presented in this book. The fuzzy theory is a mathematical concept and, at the same time, it is applied to many versatile engineering fields and research domains related to computer science. The fuzzy system offers some knowledge about uncertainty and is also related to the theory of probability. A fuzzy logic-based model acts as the classifier for many different types of data belonging to several classes. Covered in this book are topics such as the fundamental concepts of mathematics, fuzzy logic concepts, probability and possibility theories, and evolutionary computing to some extent. The combined fields of neural network and fuzzy domain (known as the neuro-fuzzy system) are explained and elaborated. Each chapter has been produced in a very lucid manner, with grading from simple to complex to accommodate the anticipated different audiences. The application-oriented approach is the unique feature of this book. Audience This book will be read and used by a broad audience including applied mathematicians, computer scientists, and industry engineers.

The world we live in is pervaded with uncertainty and imprecision. Is it likely to rain this afternoon? Should I take an umbrella with me? Will I be able to find parking near the campus? Should I go by bus? Such simple questions are a c- mon occurrence in our daily lives. Less simple examples: What is the probability that the price of oil will rise sharply in the near future? Should I buy Chevron stock? What are the chances that a bailout of GM, Ford and Chrysler will not s- ceed? What will be the consequences? Note that the examples in question involve both uncertainty and imprecision. In the real world, this is the norm rather than exception. There is a deep-seated tradition in science of employing probability theory, and only probability theory, to deal with uncertainty and imprecision. The mon- oly of probability theory came to an end when fuzzy logic made its debut. H- ever, this is by no means a widely accepted view. The belief persists, especially within the probability community, that probability theory is all that is needed to deal with uncertainty. To quote a prominent Bayesian, Professor Dennis Lindley, “The only satisfactory description of uncertainty is probability.

Nowadays, voluminous textbooks and monographs in fuzzy logic are devoted only to separate or some combination of separate facets of fuzzy logic. There is a lack of a single book that presents a comprehensive and self-contained theory of fuzzy logic and its applications. Written by world renowned authors, Lofti Zadeh, also known as the Father of Fuzzy Logic, and Rafik Aliev, who are pioneers in fuzzy logic and fuzzy sets, this unique compendium includes all the principal facets of fuzzy logic such as logical, fuzzy-set-theoretic, epistemic and relational. Theoretical problems are prominently illustrated and illuminated by numerous carefully worked-out and thought-through examples. This invaluable volume will be a useful reference guide for academics, practitioners, graduates and undergraduates in fuzzy logic and its applications.

Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.

Fuzzy logic is a relatively new concept in science applications. Hitherto, fuzzy logic has been a conceptual process applied in the field of risk management. Its potential applicability is much wider than that, however, and its particular suitability for expanding our understanding of processes and information in science and engineering in our post-modern world is only just beginning to be appreciated. Written as a companion text to the author’s earlier volume "An Introduction to Fuzzy Logic Applications", the book is aimed at professional engineers and students and those with an interest in exploring the potential of fuzzy logic as an information processing kit with a wide variety of practical applications in the field of engineering science and develops themes and topics introduced in the author’s earlier text.

No previous knowledge of fuzzy set theory and fuzzy logic is required for understanding the material covered in the book. Although knowledge of basic ideas of classical (nonfuzzy) set theory and classical (two-valued) logic is useful, fundamentals of these subject areas are briefly overviewed in the book. In addition, basic ideas of neural networks, genetic algorithms, and rough sets are also explained. This makes the book virtually self-contained.