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).
Search papers by keyword:
Paper results for keyword: ConsistencySeven is the magic number in nature
Thomas SaatyJournal: Proceedings of the American Philosophical SocietyWhere there is structure, the parts of the structure must function together with a degree of consistency and purpose. Specifically, I am thinking of dynamic systems in which there are action and reaction among the parts and their functions and also friction and resistance. Natural systems, such a...
Read MoreWhy the magic number seven plus or minus two
Thomas Saaty, Mujgan Sagir OzdemirJournal: Mathematical and computer modellingIn 1956, Miller conjectured that there is an upper limit on our capacity to process information on simultaneously interacting elements with reliable accuracy and with validity. This limit is seven plus or minus two elements. He noted that the number 7 occurs in many aspects of life, from the seve...
Read MoreDecision-making with the AHP: Why is the principal eigenvector necessary
Thomas SaatyJournal: European journal of operational researchIn this paper it is shown that the principal eigenvector is a necessary representation of the priorities derived from a positive reciprocal pairwise comparison judgment matrix A=(aij) when A is a small perturbation of a consistent matrix. When providing numerical judgments, an individual attempts...
Read MoreDeriving the AHP 1-9 scale from first principles
Thomas SaatyJournal: Proceedings of the Sixth International Symposium on the Analytic Hierarchy ProcessWe demonstrate how the integers 1 to 9 used in the Fundamental Scale of the AHP to represent pairwise comparison judgments can be derived from stimulus-response theory. The conditions required for the stability of the eigenvector of priorities, known from the mathematics literature, are briefly m...
Read MoreRatio scales derived from perturbations of consistent judgments
Thomas SaatyJournal: BehaviormetrikaWe derive ratio scales from paired comparison judgments in a reciprocal matrix A. When the judgments are consistent, we have a principal eigenvalue structure which is preserved when A is perturbed. Mathematical conditions are given on the size of the perturbations to produce a good approximation ...
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 MoreComparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios
Thomas Saaty, Luis VargasJournal: Mathematical modellingThree 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...
Read MoreApplications of the Analytic Hierarchy Process to long range planning processes
James Emshoff, Thomas SaatyJournal: European Journal of Operational ResearchThis paper considers the long range planning process from the point of view both of projecting forward likely or desired changes from the current position to define a possible future state, and of identifying desirable future states and working backwards from those to consider ways in which they ...
Read MoreConsistency & Compatibility, Two sides of the same coin
Claudio GarutiJournal: International Symposium on the Analytic Hierarchy Process 2016In MCDM to have an index of consistency for pair comparison matrices is a very important matter. This index may help to produce better metrics and of course better answers to the problem, which is the final purpose of majority of the MCDM methods. To illustrate the relevance of this matter, this ...
Read More
Seven is the magic number in nature
Thomas SaatyJournal: Proceedings of the American Philosophical SocietyWhere there is structure, the parts of the structure must function together with a degree of consistency and purpose. Specifically, I am thinking of dynamic systems in which there are action and reaction among the parts and their functions and also friction and resistance. Natural systems, such a...
Read MoreWhy the magic number seven plus or minus two
Thomas Saaty, Mujgan Sagir OzdemirJournal: Mathematical and computer modellingIn 1956, Miller conjectured that there is an upper limit on our capacity to process information on simultaneously interacting elements with reliable accuracy and with validity. This limit is seven plus or minus two elements. He noted that the number 7 occurs in many aspects of life, from the seve...
Read MoreDecision-making with the AHP: Why is the principal eigenvector necessary
Thomas SaatyJournal: European journal of operational researchIn this paper it is shown that the principal eigenvector is a necessary representation of the priorities derived from a positive reciprocal pairwise comparison judgment matrix A=(aij) when A is a small perturbation of a consistent matrix. When providing numerical judgments, an individual attempts...
Read MoreDeriving the AHP 1-9 scale from first principles
Thomas SaatyJournal: Proceedings of the Sixth International Symposium on the Analytic Hierarchy ProcessWe demonstrate how the integers 1 to 9 used in the Fundamental Scale of the AHP to represent pairwise comparison judgments can be derived from stimulus-response theory. The conditions required for the stability of the eigenvector of priorities, known from the mathematics literature, are briefly m...
Read MoreRatio scales derived from perturbations of consistent judgments
Thomas SaatyJournal: BehaviormetrikaWe derive ratio scales from paired comparison judgments in a reciprocal matrix A. When the judgments are consistent, we have a principal eigenvalue structure which is preserved when A is perturbed. Mathematical conditions are given on the size of the perturbations to produce a good approximation ...
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 MoreComparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios
Thomas Saaty, Luis VargasJournal: Mathematical modellingThree 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...
Read MoreApplications of the Analytic Hierarchy Process to long range planning processes
James Emshoff, Thomas SaatyJournal: European Journal of Operational ResearchThis paper considers the long range planning process from the point of view both of projecting forward likely or desired changes from the current position to define a possible future state, and of identifying desirable future states and working backwards from those to consider ways in which they ...
Read MoreConsistency & Compatibility, Two sides of the same coin
Claudio GarutiJournal: International Symposium on the Analytic Hierarchy Process 2016In MCDM to have an index of consistency for pair comparison matrices is a very important matter. This index may help to produce better metrics and of course better answers to the problem, which is the final purpose of majority of the MCDM methods. To illustrate the relevance of this matter, this ...
Read More