Showing papers by "Thomas L. Saaty published in 2014"

How Many Judges Should There Be in a Group

Abstract: This paper briefly examines the question of how many judges are needed to obtain valid and consistent judgments when using the analytic hierarchy process. It turns out that if a judge is experienced and well versed in an area, he can be sufficient to provide the judgments instead of diluting his accuracy with the participation of others who may not be as good. How to discover such a person requires criteria used to judge his adequacy and that of others.

Analytic Heirarchy 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

An analytic hierarchy process model of group consensus

Abstract: In group decision making, a certain degree of consensus is necessary to derive a meaningful and valid outcome. This paper proposes a consensus reaching model for a group by using the Analytic Hierarchy Process (AHP). It supports people to improve their group consensus level through an updating of their judgments. In this model, a moderator suggests the most discordant decision maker to update his judgment in each step. The proposed consensus reaching model allows decision makers to accept or reject the suggestion from the moderator. This model ensures that the judgment updating is effective and the final solution will be of acceptable consistency. Finally, a numerical example is given to illustrate the validity of the proposed consensus reaching model.

Ranking Countries by Medal Priorities Won in the 2014 Sochi Winter Olympics

Abstract: The total number of gold, silver and bronze medals won by each country in the Olympics is often regarded as an indicator of that country’s winning rank. However, the values of the medals differ according to the order in which they are won in each event. One reason why it is done this way is that there has not been a scientific way to assign an appropriate priority for each type of medal which so far has been treated as an intangible. Sometimes people have used the ordinal numbers 3, 2, 1 to rank the medals, but adding ordinals has no arithmetic legitimacy because ordinals cannot be added or multiplied. Here we use the mathematical theory, the analytic hierarchy process, for the measurement of intangibles to quantify the priorities of different games according to environmental and people factors and also quantify the priorities of gold, silver and bronze medals, and then use these priorities to compute the total scores of all three types of medals won by each country in order to determine the ranking of the countries which won medals in the 22nd Winter Olympics held February 07–23, 2014, in Sochi, Russia.

Questions and Answers: Valentina Ferretti Interviews Tom Saaty

Abstract: The following interview aims to stimulate the discussion about the key characteristics of Multicriteria Analysis techniques. In particular, the interview will work through the conceptual lens of decision processes taking place in the field of urban and territorial transformations.http://dx.doi.org/10.13033/ijahp.v6i1.235

The Three Laws of Thought, Plus One: The Law of Comparisons

Abstract: The rules of logic are nearly 2500 years old and date back to Plato and Aristotle who set down the three laws of thought: identity, non-contradiction, and excluded middle. The use of language and logic has been adequate for us to develop mathematics, prove theorems, and create scientific knowledge. However, the laws of thought are incomplete. We need to extend our logical system by adding to the very old laws of thought an essential yet poorly understood law. It is a necessary law of thought that resides in our biology even deeper than the other three laws. It is related to the rudiments of how we as living beings, and even nonliving things, respond to influences as stimuli. It helps us discriminate between being ourselves and sensing that there is something else that is not ourselves that even amoebas seem to know. It is the intrinsic ability to sense and distinguish. This fourth law is the law of comparisons. Although it has been missing from our logical deductions it underlies the other three laws of thought because without it we cannot know what is and what is not.