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, with contributions from 15 experts in probability and fuzzy logic, is an exception. The contributing 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.
Use of this book is not restricted to a specific course or application. It can be used in teaching probability, fuzzy logic, general problem solving, or in any course in which probability and fuzzy logic are not normally taught together. It has applications in control theory and artificial intelligence, knowledge acquisition/management, and risk/reliability analysis.
Contents Foreword by Lotfi A. Zadeh; Foreword by Patrick Suppes; Preface; Part I: Fundamentals; Chapter 1: Introduction; Chapter 2: Fuzzy Set Theory, Fuzzy Logic, and Fuzzy Systems; Chapter 3: Probability Theory; Chapter 4: Bayesian Methods; Chapter 5: Considerations for Using Fuzzy Set Theory and Probability Theory; Chapter 6: Guidelines for Eliciting Expert Judgment as Probabilities or Fuzzy Logic; Part II: Applications; Chapter 7: Image Enhancement: Probability Versus Fuzzy Expert Systems; Chapter 8: Engineering Process Control; Chapter 9: Structural Safety Analysis: A Combined Fuzzy and Probability Approach; Chapter 10: Aircraft Integrity and Reliability; Chapter 11: Auto Reliability Project; Chapter 12: Control Charts for Statistical Process Control; Chapter 13: Fault Tree Logic Models; Chapter 14: Uncertainty Distributions Using Fuzzy Logic; Chapter 15: Signal Validation Using Bayesian Belief Networks and Fuzzy Logic; Index.