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: ScaleExperiments on rank preservation and reversal in relative measurement
Thomas Saaty, Luis VargasJournal: Mathematical and computer modellingWe 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...
Read MoreScaling the membership function
Thomas SaatyJournal: European Journal of Operational ResearchTo scale the membership function, a method is needed that can assess the importance of elements
with respect to a property or criterion that is common among them. It is conceivable that membership should be determined in terms of several criteria tangible and intangible. The approach needed is a...
Read MoreA scaling method for priorities in hierarchical structures
Thomas SaatyJournal: Journal of mathematical psychologyThe purpose of this paper is to investigate a method of scaling ratios using the principal eigenvector of a positive pairwise comparison matrix. Consistency of the matrix data is defined and measured by an expression involving the average of the nonprincipal eigenvalues. We show that λmax = n is ...
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
Experiments on rank preservation and reversal in relative measurement
Thomas Saaty, Luis VargasJournal: Mathematical and computer modellingWe 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...
Read MoreScaling the membership function
Thomas SaatyJournal: European Journal of Operational ResearchTo scale the membership function, a method is needed that can assess the importance of elements with respect to a property or criterion that is common among them. It is conceivable that membership should be determined in terms of several criteria tangible and intangible. The approach needed is a...
Read MoreA scaling method for priorities in hierarchical structures
Thomas SaatyJournal: Journal of mathematical psychologyThe purpose of this paper is to investigate a method of scaling ratios using the principal eigenvector of a positive pairwise comparison matrix. Consistency of the matrix data is defined and measured by an expression involving the average of the nonprincipal eigenvalues. We show that λmax = n is ...
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