Probability Applications

Parti
Fundamentals
JaneM. Booker
1.1 Chapters 1-6
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.
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