uman decision making is traditionally intuitive and based largely on experience and expertise. Normally, this process requires both qualitative and numerical data, but in the end, intuitive feelings about a dilemma lead to the decision. Many theories try to explore the nature of this intuitive process, but at this point all we know is that it normally works!

At first glance, computer decision making is much simpler to understand, because it is based wholly on numerical criteria. When should a stock be sold? When the current price falls below a particular value. When is a contaminated soil site undergoing remediation considered clean? When all the sensors at the site report levels of contaminant below a certain critical value. When should an alarm system go off? When the temperature exceeds a certain value. However, the stock decline may be a result of a general decline in prices; the recorded sensor values, although low, may result from seepage of hazardous material to the bottom of the aquifer from whence it will slowly pollute the water in the future; and the temperature may have been sensed exactly when someone was lighting a cigar. Generally speaking, making a computer "smart" is a nontrivial task because we must be able to foresee such possibilities as the need to account for other stock prices, dense contaminants, and cigar smoking and somehow make the computer take these factors into account.

Automated decision making is a process of determining and carrying out an act in response to a given input; the determination is made among many responses to inputs that may vary substantially. The actual input will normally be a string of numbers. The key component of such a process is the mathematical algorithm that must determine what to do in response to the input. Some common problems facing the algorithm writer are the following:

• How do we measure the input string to determine our response?

• How do we determine whether the chosen response corresponds to what we intuitively wish to happen?

• How do we take noise and uncertainty into account?

• How do we make use of other possibly non-numerical and sometimes subjective information in our decision-making process?

• How do we take into account contradictory sensory input and still reach a decision on what to do?

The first problem is related to the classic question, "How big is big?" It suggests the need to define a size estimate or "norm" for our inputs.

The solution to problem b is often the most difficult to determine. Commonly, automated decision systems are developed to meet problems arising in emergencies, for which actual tests are not possible (e.g., explosions or fires). To address this point, detailed simulations of the system of interest must be combined, if possible, with extensive human input.

The noise and uncertainty of problem c are constant companions to all systems. The combined effect of all things that are either of unknown form or origin or arise from known effects can be regarded as noise. It is generally treated by tools

of probability. Uncertainty refers to varying degrees of belief about various features of a process. For example, given a variety of sensors for measuring temperature at a point, measurement by one sensor may be believed more accurate than that by another. The actual belief can be assigned using the tools of fuzzy analysis in which numerical estimates of belief are blended with our expertise.

Problems d and e are probably the key difficulties of artificial intelligence today. To deal with d, we develop "expert systems" in which the rules to be followed, such as when to sell stocks, are implemented in accordance with the advice of an expert in the field. Problem e arises when two experts give opposing opinions about what is going on or what policy is to be followed. Although criteria abound for reaching decisions based on multiple sources of information, the area is still at the stage of basic research and trial.

Considering the exponential growth of computing power, it seems certain that number and logic "crunching" will be less of a source of computing difficulties. But it is equally clear that, as we turn to the computer to make decisions in real time, we will have little choice but to confront the problems raised here and to develop new mathematical tools to deal with them.