Part I Fundamentals from "fuzzy Logic and Probability Applications: Bridging the Gap" I.2 Suggested Reading from "fuzzy Logic and Probability Applications: Bridging the Gap"

To bridge the gap between probability and fuzzy theories, the first step is to examine and understand the two sides of the gap. The first part of this book consists of six chapters that lay the foundations of both theories and provide the fundamental principles for constructing the bridge. We (the editors) begin (in Chapter 1) with an introduction to the history of both theories and the stories describing the formulation of the gap between them. It is our intent to represent both “sides,’’ but with the tone of reconciliation. There are cases where applications support one theory more than the other, and these are brought forth in the application chapters in Part II. There are also cases where either probability or fuzzy theory is useful or a hybrid approach combining the two is best, particularly when characterizing different kinds of uncertainties in a complex problem. Following the philosophical discussion in Chapter 1, Chapters 2 and 3 provide the foundations of fuzzy theory and probability theory, respectively. Chapter 4 is devoted to Bayesian probability theory. Bayes’ theorem provides a powerful structure for bridging the gap between fuzzy and probability theory and lays some of the groundwork for the bridging mechanism. Chapter 5 then completes the building of the bridge in a mathematical and philosophical sense. Because data and information in today’s world often reside within the experience and knowledge of the human mind, Chapter 6 examines the formal use of eliciting and analyzing expert judgment. That topic comprises an entire book in its own right (Meyer and Booker, 2001). The contents of this chapter not only covers both theories but provides applications, making it the perfect transition chapter to the applications chapters in Part II.