Fuzzy Sets, Decision Making, and Expert Systems

We shall consider two versions of a decision, the classical choice model of normative decision theory (definition 1.1) and the “evaluation model” described in the first part of chapter 1.

In chapter 2 we have been concerned with decisions of individuals, that is, an individual decision maker selects a strategy or action among the available or feasable courses of actions. He does this either under certainty—in which case his choice is deterministicly limited by the anonymous “state of nature”—or he makes a decision under risk or uncertainty—in which case the possible courses of action are determined stochastically by the same anonymous world for which no rationality in any sense is assumed.

In the recent past it has become more and more obvious that comparing different ways of action as to their desirability, judging the suitability of products, and determining “optimal” solutions in decision problems can in many cases not be done by using a single criterion or a single objective function. This has led to the area of Multi-Criteria Decision Making—in the framework of which numerous evaluation schemes (for instance in the areas of cost benefit analysis or marketing) have been suggested—and to the formulation of the vector-maximum problems in mathematical programming.

Many papers in the area of fuzzy sets start with statements such as “Given membership function µ _A (x) and assuming that the minimum operator is an appropriate model for the intersection of fuzzy sets.…” If fuzzy set theory is considered to be a purely formal theory, such statements are certainly acceptable, even though some kind of formal justification of these assumptions would be desirable. If, however, fuzzy set theory is used to model real phenomena and we assert these models to be true models of reality then some kind of empirical justification is absolutely necessary.

It has long been established [e.g., Newell, Simon 1972] that electronic data processing (EDP) and human decision makers complement each other in the sense that EDP is by far superior or more powerful in terms of data processing—in particular simultaneous and parallel processing—and the human is more capable, for instance, of communicating on the basis of incomplete data, in making judgments etc. The human decision maker needs the help of EDP in terms of information processing capacity and easy-access storage. But if EDP equipment is to be used for this purpose, decision problems must be modelled properly so that the models really represent the decision maker’s problems and can be understood by the machine. This normally implies that the decision maker himself knows how to solve the problem and that the solution algorithm can be modelled well enough to be programmed for the machine. In this case the solution procedure—like the information processing process called “decision”—is well defined on the machine and the data input into the program will fully determine the result of the process. We shall call such an EDP program or system Data-Based Decision Support System or, for short, DSS. Of course there are still problems for the decision maker, and the case in which all algorithmic features are well defined is only a limiting case. The decision maker still has problems with obtaining all the data and feeding them into the computer in the correct format.