Papers

Thomas Saaty, Luis Vargas
Journal: European Journal of Pure and Applied Mathematics
The nervous system uses its own kind of mathematical function patterns for both external and internal realities. The conscious part of the nervous system is there to respond to what happens outside by regulating externally received information signals from the senses and the skin and muscles of t...

Thomas Saaty, Luis Vargas, H. J. Zoffer
Journal: Decision Analytics
While the Israeli–Palestinian conflict has raged for decades, in all of its ramifications there has never been a totally structured or scientific approach to the conflict with all of its details. The Analytic Hierarchy Process (AHP) approaches the problem along these lines. There are a plethora o...

Thomas Saaty, Luis Vargas
Journal: Social Choice and Welfare
Preferences in Arrow’s conditions are ordinal. Here we show that when intensity of preference represented by reciprocal pairwise comparisons is considered, it is always possible to construct an Arrowian social welfare function using a two-stage social choice process. In stage 1, the individual pa...

Thomas Saaty, Luis Vargas
We present an alternative process to address the Israeli Palestinian conflict. It does so in two ways that are different from past efforts. The first is by formally structuring the conflict and the second is the manner in which discussions are conducted and conclusions drawn.

Thomas Saaty, Luis Vargas
Journal: Social Choice and Welfare
Preferences in Arrow’s conditions are ordinal. Here we show that when intensity of preference represented by reciprocal pairwise comparisons is considered, it is always possible to construct an Arrowian social welfare function using a two-stage social choice process. In stage 1, the individual pa...

Thomas Saaty, Luis Vargas, Rozann Whitaker
Journal: International Journal of the Analytic Hierarchy Process
The paper provides an overview that covers the main criticisms of the AHP and the authors replies to them. Because there have been many papers that reply to criticisms, the thrust here is to classify them and reply to them briefly in each category without giving lengthy repetitions of what is alr...

Thomas Saaty, Luis Vargas
Journal: Mathematical and Computer Modelling
To achieve a decision with which the group is satisfied, the group members must accept the judgments, and ultimately the priorities. This requires that (a) the judgments be homogeneous, and (b) the priorities of the individual group members be compatible with the group priorities. There are three...

Thomas Saaty, Luis Vargas
Journal: International Journal of Management and Decision Making
In this short paper it is shown that care is required to perform the appropriate normalisation needed to derive the right set of priorities from paired comparisons when criteria are added or deleted in a decision problem. This is particularly true for criteria with respect to which the alternativ...

Thomas Saaty, Luis Vargas
Journal: International Journal of Information Technology & Decision Making
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 i...

Thomas Saaty, Luis Vargas, Klaus Dellmann
Journal: Socio-Economic Planning Sciences
An intangible is an attribute that has no scale of measurement. Intangibles such as effort and skill arise in conjunction with resource allocation but are not usually included directly in a mathematical model because of the absence of a unit of measurement. However, intangibles can be quantified ...

Thomas Saaty, Luis Vargas
Journal: Models, Methods, Concepts & Applications of the Analytic Hierarchy Process
In this paper, we used a decision making tool, the Analytic Hierarchy Process (AHP), to analyze a decision to select a trade status for China that is in the best interest of the United States before that decision came before Congress for a vote.

Thomas Saaty, Luis Vargas
Journal: Operations Research
Judgments are needed in medical diagnosis to determine what tests to perform given certain symptoms. For many diseases, what information to gather on symptoms and what combination of symptoms lead to a given disease are not well known. Even when the number of symptoms is small, the required numbe...

Thomas Saaty, Luis Vargas
Journal: Mathematical and Computer modelling
Following earlier work on neural firing and synthesis, we use the expressions we derived elsewhere in the literature for that purpose, to show how we can represent images and sounds with the aid of CLOS (Common Lisp Object System) computer program of the LISP computer language.

Thomas Saaty, Luis Vargas
Journal: Proceedings of the Fourth International Symposium on the Analytic Hierarchy Process (ISAHP’96)
We examine some examples where the use of cardinal preferences solves problems that occur when ordinal preferences are used exclusively. Ordinal preferences are the first step toward ranking alternatives but they are not the last. In general we are interested in deriving a consistent ranking of a...

Thomas Saaty, Luis Vargas
Journal: Mathematical and computer modelling
In this note, we give examples of the use of linear combinations of impulse response functions to represent visual images. We also derive expressions for estimating the parameters of these functions using the Fourier transform of stimuli.

Thomas Saaty, Luis Vargas
Journal: Journal of Mathematical Psychology
Neurons are decision makers that decide from instant to instant whether to fire or not to fire based on information received through neurotransmitter electric charge. In firing they accomplish two goals. First, they pass information to other neurons which in their turn make a decision to fire or ...

Thomas Saaty, Luis Vargas
Journal: Mathematical and computer modelling
We show through simulation that three methods of scaling, distributive (uniqueness is important), ideal (uniqueness is not important), and utility (use of interval scales for the ideal) modes, yield the same ranking of alternatives with surprisingly high frequency, except for the case of copies o...

Thomas Saaty, Luis Vargas
Journal: Applied Mathematics Letters
We extend our earlier work on positive reciprocal kernels of Fredholm integral operators [9] to study firings and their synthesis in neural networks. First, we show that, in general, neural response in both spontaneous and non-spontaneous firing give rise to generalized functions of the Dirac t...

Thomas Saaty, Luis Vargas
Journal: The Logic of Priorities
The domestic strife in South Africa between ruling whites and subordinated blacks threatens to become a major conflict of violent dimensions in the African continent. This strife is primarily a consequence of racial policies promulgated by the white apartheid regime. Donald Woods (1978) describes...

Thomas Saaty, Luis Vargas
Journal: European Journal of Operational Research
The Analytic Hierarchy Process uses paired comparisons to derive a scale of relative importance for alternatives. We investigate the effect of uncertainty in judgment on the stability of the rank order of alternatives. The uncertainty experienced by decision makers in making comparisons is measur...

Ami Arbel, Thomas Saaty, Luis Vargas
Journal: IEEE Transactions on Systems, Man, and Cybernetics
An approach to understanding and assessing issues concerning arms control is presented. Arms control has two main objectives: (1) decreasing the possibility of a nuclear exchange; and (2) limiting the scope and intensity of such an exchange. A framework is presented for dealing with those issues ...

Thomas Saaty, Luis Vargas
Journal: Journal of Mathematical Psychology
The paper presents a theory for constructing response scales based on the reciprocal property of paired comparisons of stimuli from the same sensory continuum. Reciprocal paired comparisons define the pair estimator function K(s, t), the kernel of a Fredholm integral equation of the second kind. ...

Thomas Saaty, Luis Vargas
Journal: Journal of Mathematical Psychology
Conditions for rank preservation in a positive reciprocal matrix that is inconsistent are provided. Three methods of deriving ratio estimates are examined: the eigenvalue, the logarithmic least squares, and the least squares methods. It is shown that only the principal eigenvector directly deals ...

Thomas Saaty, Luis Vargas
Journal: Omega
WE ARE GLAD to be finally'answering Belton and Gear's concerns expressed in their article in Omega [l]. There are two points they make in their letter. The first has to do with rank reversal, and the second with how to ask the question by minimizing fuzziness. Our response is organized into four ...

Thomas Saaty, Luis Vargas
Journal: Mathematical modelling
Three methods—the eigenvalue, logarithmic least squares, and least squares methods—used to derive estimates of ratio scales from a positive reciprocal matrix are analyzed. The criteria for comparison are the measurement of consistency, dual solutions, and rank preservation. It is shown that the e...

Thomas Saaty, Luis Vargas, Amos Barzilay
We use the analytic hierarchy process to analyze the role of subjective factors in decision making as illustrated in the Iran rescue operation. Essentially, we show that a decision maker and that decision maker's advisors may differ in their estimates on whether an action should or should not...

Thomas Saaty, Luis Vargas
Journal: The Logic of Priorities
The domestic strife in South Africa between ruling whites and subordinated blacks threatens to become a major conflict of violent dimensions in the African continent. This strife is primarily a consequence of racial policies promulgated by the white apartheid regime. Donald Woods (1978) describes...

Thomas Saaty, Luis Vargas
Journal: The Logic of Priorities
Today oil is the world’s major energy resource. It accounts for about 54 percent of the world’s total energy consumption. Because of conservation and the development of alternative resources in industrialized countries, the share of oil in the world’s total energy consumption is expected to decli...

Luis Vargas, Thomas Saaty
Journal: Industrial Marketing Management
We show that there is no single best solution in the leasing versus company ownership problem for the fleet administration industry as a whole. Because of the different styles and traditions of firms and because of the emphasis on intangibles beyond economics, a unifying framework of reference in...

Thomas Saaty, Luis Vargas
Journal: Behavioral science
In this paper we use the analytic hierarchy process to combine technical and behavioral characteristics of chess players and predict the outcome of a championship match. The method also applies to decision making in living systems at the level of the group. Our approach to prediction deals with t...

Thomas Saaty, Luis Vargas
Journal: The Logic of Priorities
A short time ago it was unthinkable and deemed an academic exercise to speak of rationing. People thought that there could be no crippling energy crisis because our energy czars and planners would presumably take our needs into their projections. Today the situation looks very different. Witness ...

Thomas Saaty, Luis Vargas
Journal: Socio-Economic Planning Sciences
We give a summary and an example of a new, systems oriented, method for estimating the input-output coefficients of a given economy. Our approach is based on pairwise comparisons among the sectors of the economy ranking them according to their priority on a ratio scale. What we obtain corresponds...