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: Pairwise comparisonContinuous pairwise comparisons
Thomas SaatyJournal: Fundamenta InformaticaeOne often assumes that comparisons are discrete and carried out in a matrix of numbers. However, our eyes and other senses perform comparisons in a continuous way by making many simultaneously. Here the mathematics of pairwise comparisons is generalized to the continuous case. It is more likely t...
Read MoreNegotiating the Israeli–Palestinian controversy from a new perspective
Thomas Saaty, H. J. ZofferJournal: Information Technology & Decision MakingIn most long-lasting conflicts, each party's grievances increase while the concessions they are willing to make decline in number, quality, and perceived value. Both parties lose sight of what they are willing to settle for, generally exaggerate their own needs, and minimize the needs of the ...
Read MoreAddressing with brevity criticism of the Analytic Hierarchy Process
Thomas Saaty, Luis Vargas, Rozann WhitakerJournal: International Journal of the Analytic Hierarchy ProcessThe 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...
Read MoreRelative 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 MoreMaking decisions in hierarchic and network systems
Thomas Saaty, Mariya SodenkampJournal: International Journal of Applied Decision SciencesThis paper summarises a mathematical theory of the measurement of both tangible and intangible factors, the Analytic Hierarchy Process (AHP) and its generalisation to dependence and feedback, the Analytic Network Process (ANP) and illustrates their application to making complex multicriteria deci...
Read MoreThe analytic hierarchy and analytic network measurement processes: applications to decisions under risk
Thomas SaatyJournal: European Journal of Pure and Applied MathematicsMathematics applications largely depend on scientific practice. In science measurement depends on the use of scales, most frequently ratio scales. A ratio scale there is applied to measure various physical attributes and assumes a zero and an arbitrary unit used uniformly throughout an applicatio...
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 MorePriority as dominance in derived measurement: Invariance of the principal eigenvector
Mujgan Sagir Ozdemir, Thomas SaatyRanking is a process of prioritization. Priorities, as measurement rather than pure guessing, can be derived from paired comparison judgments that generalize on ratios of actual measurements. Paired comparisons involve the selection of the smaller of the two objects being compared as the unit and...
Read MoreHypermatrix of the Brain
Thomas SaatyJournal: Artificial Neural Nets and Genetic AlgorithmsDecision-making, a natural and fundamental process of the brain, involves the use of pairwise comparisons. They are represented by a matrix whose entries belong to a fundamental scale, and from which an eigenvector of priorities that belongs to a ratio scale is derived. A simple decision is repre...
Read MoreRanking by eigenvector versus other methods in the Analytic Hierarchy Process
Thomas Saaty, G HuJournal: Applied Mathematics LettersCounter-examples are given to show that in decision making, different methods of deriving priority vectors may be close for every single pairwise comparison matrix, yet they can lead to different overall rankings. When the judgments are inconsistent, their transitivity affects the final outcome...
Read MorePrinciples of the Analytic Hierarchy Process
Thomas SaatyJournal: Expert judgment and expert systemsCognitive psychologists have classified thinking into two types. This division has gone by many names. Aristotle referred to it as active versus passive reason [35]; Freud [10] as secondary versus primary process thinking; and Hobbes [14] as thought with or without “designe.” More recently the di...
Read More
Continuous pairwise comparisons
Thomas SaatyJournal: Fundamenta InformaticaeOne often assumes that comparisons are discrete and carried out in a matrix of numbers. However, our eyes and other senses perform comparisons in a continuous way by making many simultaneously. Here the mathematics of pairwise comparisons is generalized to the continuous case. It is more likely t...
Read MoreNegotiating the Israeli–Palestinian controversy from a new perspective
Thomas Saaty, H. J. ZofferJournal: Information Technology & Decision MakingIn most long-lasting conflicts, each party's grievances increase while the concessions they are willing to make decline in number, quality, and perceived value. Both parties lose sight of what they are willing to settle for, generally exaggerate their own needs, and minimize the needs of the ...
Read MoreAddressing with brevity criticism of the Analytic Hierarchy Process
Thomas Saaty, Luis Vargas, Rozann WhitakerJournal: International Journal of the Analytic Hierarchy ProcessThe 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...
Read MoreRelative 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 MoreMaking decisions in hierarchic and network systems
Thomas Saaty, Mariya SodenkampJournal: International Journal of Applied Decision SciencesThis paper summarises a mathematical theory of the measurement of both tangible and intangible factors, the Analytic Hierarchy Process (AHP) and its generalisation to dependence and feedback, the Analytic Network Process (ANP) and illustrates their application to making complex multicriteria deci...
Read MoreThe analytic hierarchy and analytic network measurement processes: applications to decisions under risk
Thomas SaatyJournal: European Journal of Pure and Applied MathematicsMathematics applications largely depend on scientific practice. In science measurement depends on the use of scales, most frequently ratio scales. A ratio scale there is applied to measure various physical attributes and assumes a zero and an arbitrary unit used uniformly throughout an applicatio...
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 MorePriority as dominance in derived measurement: Invariance of the principal eigenvector
Mujgan Sagir Ozdemir, Thomas SaatyRanking is a process of prioritization. Priorities, as measurement rather than pure guessing, can be derived from paired comparison judgments that generalize on ratios of actual measurements. Paired comparisons involve the selection of the smaller of the two objects being compared as the unit and...
Read MoreHypermatrix of the Brain
Thomas SaatyJournal: Artificial Neural Nets and Genetic AlgorithmsDecision-making, a natural and fundamental process of the brain, involves the use of pairwise comparisons. They are represented by a matrix whose entries belong to a fundamental scale, and from which an eigenvector of priorities that belongs to a ratio scale is derived. A simple decision is repre...
Read MoreRanking by eigenvector versus other methods in the Analytic Hierarchy Process
Thomas Saaty, G HuJournal: Applied Mathematics LettersCounter-examples are given to show that in decision making, different methods of deriving priority vectors may be close for every single pairwise comparison matrix, yet they can lead to different overall rankings. When the judgments are inconsistent, their transitivity affects the final outcome...
Read MorePrinciples of the Analytic Hierarchy Process
Thomas SaatyJournal: Expert judgment and expert systemsCognitive psychologists have classified thinking into two types. This division has gone by many names. Aristotle referred to it as active versus passive reason [35]; Freud [10] as secondary versus primary process thinking; and Hobbes [14] as thought with or without “designe.” More recently the di...
Read More