Papers
This section presents a collection of AHP/ANP papers. Whether you are a student, academic and/or professional in the field of decision making, you can help us expand this collection by sharing your papers on decision making with the Analytic Hierarchy Process (AHP) and the Analytic Network Process (ANP).
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Paper results for keyword: EigenvalueRelative measurement and its generalization in decision making why pairwise comparisons are central in mathematics for the measurement of intangible factors the Analytic Hierarchy/Network Process
Thomas SaatyJournal: RACSAM-Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. MatematicasAccording to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which s...
Read MoreNew light on the theorem of perron
Thomas SaatyJournal: Trabajos de Estadistica Y de Investigacion OperativaWe prove that the principal eigenvector of a positive matrix represents the relative dominance of its rows of ranking of alternatives in a decision represented by the rows of a pairwise comparison matrix.
Read MoreInconsistency and rank preservation
Thomas Saaty, Luis VargasJournal: Journal of Mathematical PsychologyConditions 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 ...
Read MorePriority setting in complex problems
Thomas SaatyJournal: IEEE Transactions on Engineering ManagementThere are three principles which one can recognize in problem solving. They are the principles of decomposition, comparative judgments, and synthesis of priorities. The Analytic Hierarchy Process (AHP) provides a comprehensive framework to cope with the intuitive, the rational, and the irrational...
Read MoreMathematical modeling of dynamic decisions; priorities and hierarchies with time dependence
Thomas SaatyJournal: Mathematics and computers in SimulationThe question often arises in regard to the use of Analytic Hierarchy Process: What would one do if the judgments where to change? A simple answer to that problem is that one should solve the new problem. But this is not what people usually have in mind. Presumably what they would like is a parame...
Read MoreHigher education in the United States (1985–2000): Scenario construction using a hierarchical framework with eigenvector weighting
Thomas Saaty, Paul C. RogersJournal: Socio-Economic Planning SciencesThe object of this paper is to illustrate an application of hierarchies and eigenvalues developed by the first author to the area of planning in higher education. We start with a brief discussion of the role of scenario construction in planning and follow it with a discussion of the role of hiera...
Read MoreModeling unstructured decision problems—the theory of analytical hierarchies
Thomas SaatyJournal: Mathematics and computers in simulationQuantitative modeling of unstructured decision problems with social implications is new and challenging and has pressing needs. A new approach to scaling using largest eigenvalues and reciprocal matrices and the effect of inconsistent judgment are introduced and relevant theory discussed. In this...
Read More
Relative measurement and its generalization in decision making why pairwise comparisons are central in mathematics for the measurement of intangible factors the Analytic Hierarchy/Network Process
Thomas SaatyJournal: RACSAM-Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. MatematicasAccording to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which s...
Read MoreNew light on the theorem of perron
Thomas SaatyJournal: Trabajos de Estadistica Y de Investigacion OperativaWe prove that the principal eigenvector of a positive matrix represents the relative dominance of its rows of ranking of alternatives in a decision represented by the rows of a pairwise comparison matrix.
Read MoreInconsistency and rank preservation
Thomas Saaty, Luis VargasJournal: Journal of Mathematical PsychologyConditions 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 ...
Read MorePriority setting in complex problems
Thomas SaatyJournal: IEEE Transactions on Engineering ManagementThere are three principles which one can recognize in problem solving. They are the principles of decomposition, comparative judgments, and synthesis of priorities. The Analytic Hierarchy Process (AHP) provides a comprehensive framework to cope with the intuitive, the rational, and the irrational...
Read MoreMathematical modeling of dynamic decisions; priorities and hierarchies with time dependence
Thomas SaatyJournal: Mathematics and computers in SimulationThe question often arises in regard to the use of Analytic Hierarchy Process: What would one do if the judgments where to change? A simple answer to that problem is that one should solve the new problem. But this is not what people usually have in mind. Presumably what they would like is a parame...
Read MoreHigher education in the United States (1985–2000): Scenario construction using a hierarchical framework with eigenvector weighting
Thomas Saaty, Paul C. RogersJournal: Socio-Economic Planning SciencesThe object of this paper is to illustrate an application of hierarchies and eigenvalues developed by the first author to the area of planning in higher education. We start with a brief discussion of the role of scenario construction in planning and follow it with a discussion of the role of hiera...
Read MoreModeling unstructured decision problems—the theory of analytical hierarchies
Thomas SaatyJournal: Mathematics and computers in simulationQuantitative modeling of unstructured decision problems with social implications is new and challenging and has pressing needs. A new approach to scaling using largest eigenvalues and reciprocal matrices and the effect of inconsistent judgment are introduced and relevant theory discussed. In this...
Read More