Showing papers by "Thomas L. Saaty published in 2007"

The analytic hierarchy and analytic network measurement processes: Applications to decisions under Risk

Abstract: Mathematics applications largely depend on scientific practice. In science measurement depends on the use of scales, most frequently ratio scales. A ratio scale there is applied to measure various physical attributes and assumes a zero and an arbitrary unit used uniformly throughout an application. Different ratio scales are combined by means of formulas. The formulas apply within structures involving variables and their relations under natural law. The meaning and use of the outcome is then interpreted according to the judgment of an expert as to how well it meets understanding and experience or satisfies laws of nature that are always there. Science derives results objectively, but interprets their significance is subjectively. In decision making, there are no set laws to characterize structures in which relations are predetermined for every decision. Understanding is needed to structure a problem and then also to use judgments to represent importance and preference quantitatively so that a best outcome can be derived by combining and trading off different factors or attributes. From numerical representations of judgments, priority scales are derived and synthesized according to given rules of composition. In decision making the priority scales can only be derived objectively after subjective judgments are made. The process is the opposite of what we do in science. This paper summarizes a mathematical theory of measurement in decision making and applies it to real-life examples of complex decisions.

Group decision-making: Head-count versus intensity of preference

Abstract: This paper puts forth a framework for reshaping the group decision-making process. The proposed framework extends from the usual one-issue-at-a-time decision-making to one that involves several related issues simultaneously. Weaknesses of the traditional majority voting mechanism are first identified, and then a different voting method that takes each individual voter's sentiment into account is discussed. Specifically, a decision-maker is asked to express his/her intensity of preference for the issues encountered. Three hierarchical structures—benefits, costs, and risks—are developed to evaluate the alternatives. Due to the nature of pairwise comparisons and synthesis, the proposed method is amenable to consensus building and has higher reliability and consistency. It can be used for candidate selection, e.g. governmental election, when a large population is involved. It is also effective for resource allocation and prioritization when a small group or business is concerned. We believe the proposed approach has potential for resolving deficiencies of the conventional voting mechanism, and can be applied to many real-world problems. Its implementation on the Internet is also discussed.