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: Ratio ScaleRatio Scales are Critical for Modeling Neural Synthesis in the Brain
Thomas SaatyJournal: Artificial Neural Nets and Genetic AlgorithmsThe brain generally miniaturizes its perceptions into what may be regarded as a model of what happens outside. We experience the world according to the capacity of our nervous system to register the stimuli we receive. In order to understand and control the environment there needs to be proportio...
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 MoreThe seven pillars of the Analytic Hierarchy Process
Thomas SaatyJournal: Multiple Criteria Decision Making in the New Millennium The seven pillars of the AHP, some highlights of which are discussed in the paper, are: 1) ratio scales derived from reciprocal paired comparisons; 2) paired comparisons and the psychophysical origin of the fundamental scale used to make the comparisons; 3) conditions for sensitivity of the eigen...
Read MoreThat is not the Analytic Hierarchy Process: what the AHP is and what it is not
Thomas SaatyJournal: Journal of Multi‐Criteria Decision AnalysisThere are two basic principles that are totally missed by Salo and Hamalaninen in their attempt to reformulate the AHP, which is based on ratio scales, to fit multiattribute value theory, which is based on interval scales.
Read MoreRatio scales are fundamental in decision making
Thomas SaatyJournal: Proceedings of the Fourth International Symposium on the Analytic Hierarchy Process (ISAHP’96)Multicriteria decision making depends On the use of numbers and scales to make trade-offs. We examine in detail the types of numerical scales of measurement there are and which ones seem to work better for measurement in a hierarchic model of a complex problem. It is argued that ratio scales play...
Read MoreThe Analytic Hierarchy Process and utility theory: Ratio scales and interval scales
Rozann SaatyJournal: Proceedings of the Fourth International Symposium on the Analytic Hierarchy Process (ISAHP’96)This paper is a brief summary of the successful workability of the Analytic Hierarchy Process (All!') free of problems and paradoxes. As a theory of ratio scale measurement, the AHP has found multiple and diverse applications in priority setting, decision making, planning , resource allocatio...
Read MoreA ratio scale metric and the compatibility of ratio scales: The possibility of arrow's impossibility theorem
Thomas SaatyJournal: Applied Mathematics LettersWe develop a metric for ratio scales and explore the notion of compatibility of two sets of measurements of a set of objects or properties on a ratio scale. We briefly address Arrow's impossibility theorem. We maintain that it is not as impossible as claimed when, as in reality, a certain degree ...
Read MoreWhat is relative measurement? The ratio scale phantom
Thomas SaatyJournal: Mathematical and Computer ModellingTraditionally, measurement scales with a unit are assumed to be available to measure and rank alternatives. However, such scales are scarce and it is often desired to rank alternatives on many tangible and intangible criteria. How? Relative measurement is a method for deriving ratio scales from p...
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 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 MoreExploring optimization through hierarchies and ratio scales
Thomas SaatyJournal: Socio-Economic Planning SciencesThis paper explores the concept of optimization by solely using the AHP and compares outcomes with those obtained in traditional optimization theory without and with constraints. The difference is essentially in the absence of the traditional black box involving complex manipulations in algebra o...
Read MoreHierarchies, reciprocal matrices, and ratio scales
Thomas SaatyJournal: Discrete and System ModelsWe are interested in the problem of finding a scale which reflects the relative intensity of a property shared by n objects. The objects may be n stones and the properties may be their weights. What is needed is a theory that would enable us to conduct measurement which produces not only known re...
Read MoreApplications of analytical hierarchies
Thomas SaatyJournal: Mathematics and Computers in SimulationIn a previous article which appeared in this journal I outlined some of the ideas involved in measuring
priorities in hierarchical systems. It was my hope to show that when dealing with complexity, a hierarchical structure with ratio scale measurement provides a natural expression of the mind to...
Read MoreEstimating technological coefficients by the Analytic Hierarchy Process
Thomas Saaty, Luis VargasJournal: Socio-Economic Planning SciencesWe 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...
Read More
Ratio Scales are Critical for Modeling Neural Synthesis in the Brain
Thomas SaatyJournal: Artificial Neural Nets and Genetic AlgorithmsThe brain generally miniaturizes its perceptions into what may be regarded as a model of what happens outside. We experience the world according to the capacity of our nervous system to register the stimuli we receive. In order to understand and control the environment there needs to be proportio...
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 MoreThe seven pillars of the Analytic Hierarchy Process
Thomas SaatyJournal: Multiple Criteria Decision Making in the New Millennium The seven pillars of the AHP, some highlights of which are discussed in the paper, are: 1) ratio scales derived from reciprocal paired comparisons; 2) paired comparisons and the psychophysical origin of the fundamental scale used to make the comparisons; 3) conditions for sensitivity of the eigen...
Read MoreThat is not the Analytic Hierarchy Process: what the AHP is and what it is not
Thomas SaatyJournal: Journal of Multi‐Criteria Decision AnalysisThere are two basic principles that are totally missed by Salo and Hamalaninen in their attempt to reformulate the AHP, which is based on ratio scales, to fit multiattribute value theory, which is based on interval scales.
Read MoreRatio scales are fundamental in decision making
Thomas SaatyJournal: Proceedings of the Fourth International Symposium on the Analytic Hierarchy Process (ISAHP’96)Multicriteria decision making depends On the use of numbers and scales to make trade-offs. We examine in detail the types of numerical scales of measurement there are and which ones seem to work better for measurement in a hierarchic model of a complex problem. It is argued that ratio scales play...
Read MoreThe Analytic Hierarchy Process and utility theory: Ratio scales and interval scales
Rozann SaatyJournal: Proceedings of the Fourth International Symposium on the Analytic Hierarchy Process (ISAHP’96)This paper is a brief summary of the successful workability of the Analytic Hierarchy Process (All!') free of problems and paradoxes. As a theory of ratio scale measurement, the AHP has found multiple and diverse applications in priority setting, decision making, planning , resource allocatio...
Read MoreA ratio scale metric and the compatibility of ratio scales: The possibility of arrow's impossibility theorem
Thomas SaatyJournal: Applied Mathematics LettersWe develop a metric for ratio scales and explore the notion of compatibility of two sets of measurements of a set of objects or properties on a ratio scale. We briefly address Arrow's impossibility theorem. We maintain that it is not as impossible as claimed when, as in reality, a certain degree ...
Read MoreWhat is relative measurement? The ratio scale phantom
Thomas SaatyJournal: Mathematical and Computer ModellingTraditionally, measurement scales with a unit are assumed to be available to measure and rank alternatives. However, such scales are scarce and it is often desired to rank alternatives on many tangible and intangible criteria. How? Relative measurement is a method for deriving ratio scales from p...
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 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 MoreExploring optimization through hierarchies and ratio scales
Thomas SaatyJournal: Socio-Economic Planning SciencesThis paper explores the concept of optimization by solely using the AHP and compares outcomes with those obtained in traditional optimization theory without and with constraints. The difference is essentially in the absence of the traditional black box involving complex manipulations in algebra o...
Read MoreHierarchies, reciprocal matrices, and ratio scales
Thomas SaatyJournal: Discrete and System ModelsWe are interested in the problem of finding a scale which reflects the relative intensity of a property shared by n objects. The objects may be n stones and the properties may be their weights. What is needed is a theory that would enable us to conduct measurement which produces not only known re...
Read MoreApplications of analytical hierarchies
Thomas SaatyJournal: Mathematics and Computers in SimulationIn a previous article which appeared in this journal I outlined some of the ideas involved in measuring priorities in hierarchical systems. It was my hope to show that when dealing with complexity, a hierarchical structure with ratio scale measurement provides a natural expression of the mind to...
Read MoreEstimating technological coefficients by the Analytic Hierarchy Process
Thomas Saaty, Luis VargasJournal: Socio-Economic Planning SciencesWe 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...
Read More