Showing papers by "Thomas L. Saaty published in 2005"

Analytic Hierarchy Process

Abstract: The Analytic Hierarchy Process (AHP) is a theory of relative measurement of intangible criteria. With this approach to relative measurement, a scale of priorities is derived from pairwise comparison measurements only after the elements to be measured are known. The ability to do pairwise comparisons is our biological heritage and we need it to cope with a world where everything is relative and constantly changing and thus, there are no fixed standards to measure things on. In traditional measurement, one has a scale that one applies to measure any element that comes along that has the property the scale is for, and the elements are measured one by one, not by comparing them with each other. In the AHP, paired comparisons are made with judgments using numerical values taken from the AHP absolute fundamental scale of 1 to 9. A scale of relative values is derived from all these paired comparisons and it also belongs to an absolute scale that is invariant under the identity transformation like the system of real numbers. The AHP is useful for making multicriteria decisions involving benefits, opportunities, costs, and risks. The ideas are developed in stages and illustrated with examples of real-life decisions. The subject is transparent and easy to understand why it is done the way it is along the lines discussed here. The AHP has a generalization to dependence and feedback; the Analytic Network Process (ANP) is not discussed here. Keywords: analytic hierarchy process; decision making; prioritization; benefits; costs; complexity

Making and validating complex decisions with the ahp/anp

Abstract: Several examples that serve to validate the AHP/ANP with matrices hierarchies and networks are given in this paper. They are then followed by a discussion of the real numbers and how they are generated without the need for an absolute zero, and how they define an absolute scale of measurement that also does not need an absolute zero. In the AHP/ANP the measurement of an alternative depends on what other alternatives it is compared with. The result is that rank can change if alternatives are added or deleted, something that does not occur in one-at-a-time rating of the alternatives by comparing them with an ideal. An example is provided to show that this is natural and need not involve new criteria or change in judgments. A brief discussion of Utility Theory, the other multi-criteria theory, which uses interval scales to measure intangibles and some of its problems and paradoxes, is given. The references at the end include most of the papers that are adverse to the AHP with brief comments about several of them given in the paper.

The possibility of group welfare functions

Abstract: This paper gives a brief overview of the well-known impossibility-possibility theorem in constructing a social welfare function from individual functions. The Analytic Hierarchy Process uses a fundamental scale of absolute numbers to represent judgments about dominance in paired comparisons. It is shown that it is possible to derive such a function in two ways. One is from the synthesized functions of the judgments of each of the individuals. The other is obtained by first combining corresponding pairwise comparison judgments made by all the individuals, thus obtaining a matrix of combined judgments for the group and then deriving a welfare function for the group. With consistency the four conditions imposed by Arrow are satisfied. With inconsistency, an additional condition is needed.