represent the problem as thoroughly as possi- ble, but not so thoroughly as to lose sensitivity to change in the elements;
consider the environment surrounding the problem;
identify the issues or attributes that contribute to the solution;
and identify the participants associated with the problem.
Arranging the goals, attributes, issues, and stake- holders in a hierarchy serves two purposes. It provides an overall view of the complex relation- ships inherent in the situation; and helps the deci- sion maker assess whether the issues in each level are of the same order of magnitude, so he can compare such homogeneous elements accurately.
One certainly cannot compare according to size a football with Mr. Everest and have any hope of getting a meaningful answer. The football and Mt. Everest must be compared in sets of objects of their class. Later we give a fundamental scale of use in making the comparison. It consists of verbal judgments ranging from equal to extreme (equal, moderately more, strongly more, very strongly more, extremely more) corresponding to the verbal judgments are the numerical judgments (1, 3, 5, 7, 9) and compromises between these values. We have completed compiling a dictionary of hier- archies pertaining to all sorts of problems, from personal to corporate to public.
A hierarchy does not need to be complete, that is, an element in a given level does not have to function as an attribute (or criterion) for all the elements in the level below. A hierarchy is not the traditional decision tree. Each level may represent a different cut at the problem. One level may represent social factors and another political fac- tor to be evaluated in terms of the social factors or vice versa. Further, a decision maker can insert or eliminate levels and elements as necessary to clarify the task of setting priorities or to sharpen the focus on one or more parts of the system. Elements that have a global character can be represented at the higher levels of the hierarchy, others that specifically characterize the problem at hand can be developed in greater depth. The task of setting priorities requires that the criteria, the properties or features of the alternatives being compared, and the alternatives themselves are gradually layered in the hierarchy so that it is meaningful to compare them among themselves in relation to the elements of the next higher level. Finally, after judgments have been made on the impact of all the elements and priorities have been computed for the hierarchy as a whole, sometimes, and with care, the less important elements can be dropped from further consideration because of their relatively small impact on the overall objec- tive. The priorities can then be recomputed throughout, either with or without changing the remaining judgments.