TABLE OF CONTENTS Over the years, we have increasingly been on the search to understand the human ability to reason and make decisions, often in the face of only partial knowledge. The ability to generalize from limited experience into areas as yet encountered is one of the fascinating abilities of the human mind. Traditionally, our attempt to understand the world and its functions has been limited to finding mathematical models or equations for the systems under study. This approach has proven extremely useful, particularly in an age when very fast computers are available to most of us with only a minimum amount of capital outlay. And even when these computers are not fast enough, many researchers can gain access to super computers capable of giving numerical solutions to multiorder differential equations that are capable of describing most of the industrial processes.
This analytical enlightenment, however, has come at the cost of realizing just how complex the world is. At this point, we have come to realize that no matter how simple the system is, we can never hope to model it completely. So instead, we select suitable approximations that give us answers that we think, are sufficiently precise. Because our models are incomplete, we are faced with one of the following choices:
Use the approximate model and introduce probabilistic representations to allow for the possible errors.
Seek to develop an increasingly complex model in the hope that we can...
