Showing papers by "Thomas L. Saaty published in 1990"

An exposition of the AHP in reply to the paper “remarks on the analytic hierarchy process”

Abstract: It is a fact that people make decisions and have been making decisions for a very long time. Contrary to what some of us who are interested in decision-making may like to believe, most people do not take seriously the existence of theories which purport to set their thinking and feeling right. They claim to know their own value system and what they want. They may wonder how anyone else can know well enough to tell them how best to organize their thinking in order to make better choices. Yet, research has shown that complex decisions are beyond the capacity of the brain to synthesize intuitively and efficiently. Since decision making is a natural characteristic of people, how do we describe what they do so that an ordinary mortal can understand what we are saying? We do not wish to legislate the method with which people should make decisions, but only to describe it even when it is prescribed by some method. In the process, we may learn things that can help people make better decisions. How? The Analytic Hierarchy Process (AHP) (Forman et al., Harker 1986, Harker and Vargas 1987, Saaty 1986, 1988a, b, Saaty and Vargas 1987, Xu 1988, Golden et al. 1989, Saaty and Alexander 1989) is a theory of measurement. When applied in decision making it assists one to describe the general decision operation by decomposing a complex problem into a multi-level hierarchic structure of objectives, criteria, subcriteria and alternatives. The AHP provides a fundamental scale of relative magnitudes expressed in dominance units to represent judgments in the form of paired comparisons. A ratio scale of relative magnitudes expressed in priority units is then derived from each set of comparisons. An overall rcatio scale of priorities is then synthesized to obtain a ranking of the alternatives. From its axioms to its procedures, the AHP has turned out to be historically and theoretically a different and independent theory of decision making from utility theory. Much as a dialogue evolved in mathematics around the consistency of different geometries and around absolute and relative space and time in physics, both to dispel absolute notions, those who believe that only utility theory can tell us the absolute truth about man's decision-making might take a close look at the AHP. It has found varied and serious applications. It also has a particular way of generating ratio scales and dealing with inconsistency in judgment that have contributed to its effectiveness in resource allocation and in the setting of priorities by a group of decision makers. Utility theory is a normative process. The AHP as a descriptive theory encompasses procedures leading to outcomes as would be ranked by a normative theory. But it must go beyond to deal with outcomes not accounted for by the demanding assumptions of a normative theory. We must briefly describe the AHP to enable the reader to see that a practicable theory based on ratio scales need not dilute itself to satisfy expectations of people who derive their understanding from a theory based on interval scales. This is particularly true if the rival theory, in aspiring for generality, also makes unrealistic assumptions, for example about the transitivity and consistency of preferences and the difficult use of lotteries,

The analytic hierarchy process in conflict management

Abstract: The Analytic Hierarchy Process (AHP) is a theory of measurement. When applied in decision‐making, it assists one to describe the general decision operation by decomposing a complex problem into a multi‐level hierarchic structure of objectives, criteria, subcriteria and alternatives. The AHP provides a fundamental scale of absolute magnitudes to represent judgments in the form of paired comparisons. A ratio scale of relative magnitudes expressed in priority units is then derived from each set of comparisons. An overall ratio scale of priorities is synthesized to obtain ranking of the alternatives. What is illustrated here is an application of the AHP to a retributive ongoing conflict in which the parties maximize both their benefits from and costs to the opponent. Using the AHP, benefit and cost hierarchies are constructed for the parties, four for each, involving actual and perceived benefits and costs of concessions. Similarly, a mediator must construct his own hierarchies to evaluate and propose changes in judgments and new concessions to improve an impasse in negotiation.

Ratio Scales Derived from Perturbations of Consistent Judgments

Abstract: We derive ratio scales from paired comparison judgments in a reciprocal matrix A When the judgments are consistent, we have a principal eigenvalue structure which is preserved when A is perturbed Mathematical conditions are given on the size of the perturbations to produce a good approximation to A by a matrix W of ratios formed from the derived scale Goodness is analyzed for both metric and order properties The results of this paper point strongly to the fact that the eigenvalue process is the intrinsic solution to the problem of deriving a ratio scale, thus one does not need to invent extraneous normative criteria to solve an inconsistent problem

Embracing the Future: Meeting the Challenge of Our Changing World

Abstract: The shock studying the future change order technology science the brain creativity problem solving the challenge of the future.