Procedures for synthesizing ratio judgements

Aczél, J.; Saaty, Thomas L.

doi:10.1016/0022-2496(83)90028-7

Cited by 712 publications

(329 citation statements)

References 4 publications

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“…If the individuals themselves have different priorities of importance their judgments (final outcomes) are raised to the power of their priorities and then the geometric mean is formed. The following is a summary of results of research I did with Janos Aczel many years ago [2].…”

Section: The Question Of Rank Preservation and Reversal In The Discrementioning

confidence: 99%

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

Saaty¹

2008

Rev. R. Acad. Cien. Serie A. Mat.

787

501

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According 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 scales of measurement exist. The theme of this paper is that direct comparisons are necessary to establish measurements for intangible properties that have no scales of measurement. In that case the value derived for each element depends on what other elements it is compared with. We show how relative scales can be derived by making pairwise comparisons using numerical judgments from an absolute scale of numbers. Such measurements, when used to represent comparisons can be related and combined to define a cardinal scale of absolute numbers that is stronger than a ratio scale. They are necessary to use when intangible factors need to be added and multiplied among themselves and with tangible factors. To derive and synthesize relative scales systematically, the factors are arranged in a hierarchic or a network structure and measured according to the criteria represented within these structures. The process of making comparisons to derive scales of measurement is illustrated in two types of practical real life decisions, the Iran nuclear show-down with the West in this decade and building a Disney park in Hong Kong in 2005. It is then generalized to the case of making a continuum of comparisons by using Fredholm's equation of the second kind whose solution gives rise to a functional equation. The Fourier transform of the solution of this equation in the complex domain is a sum of Dirac distributions demonstrating that proportionate response to stimuli is a process of firing and synthesis of firings as neurons in the brain do. The Fourier transform of the solution of the equation in the real domain leads to nearly inverse square responses to natural influences. Various generalizations and critiques of the approach are included. Medidas relativas y su generalización en la toma de decisiones Porqué las comparaciones dos a dos son fundamentales en matemáticas para la medida de factores intangibles El proceso analítico jerarquía/redResumen. En primer lugar se argumenta, tal como hizo Henri Lebesgue, que el establecer comparaciones directas entre objetos en relación con alguna propiedad es un proceso matemático fundamental para deducir medidas. Podemos comprobar que esta idea funciona bien para aquellas propiedades para las que se pueden construir escalas de medida. La idea fundamental de este artículo es demostrar que también se puede realizar un proceso de comparación para establecer medidas de propiedades intangibles. Se demuestra que se pueden deducir escalas relativas haciendo comparaciones por parejas, es decir dos a dos, utilizando estimaciones numéricas a partir de otra escala numérica como son los autovectores principales. Estas medidas son del todo necesarias cuando hay que determinar la tasa de intercambio ent...

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Section: The Question Of Rank Preservation and Reversal In The Discrementioning

confidence: 99%

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

Saaty¹

2008

Rev. R. Acad. Cien. Serie A. Mat.

787

501

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“…These individual preferences were aggregated by means of the geometric mean, and after applying the AHP algorithm, the cooperative preferences were set. According to Aczel and Saaty (1983) Likert scale, ranging from excellent to extremely low. For example, a member of the financial committee, after analysing sales and profit growth ratios scored as "low" the criterion "business growth".…”

Section: Prioritizationmentioning

confidence: 99%

A Credit Score System for Socially Responsible Lending

2014

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Ethical banking, microfinance institutions or certain credit cooperatives, among others, grant socially responsible loans. This paper presents a credit score system for them. The model evaluates both social and financial aspects of the borrower. The financial aspects are evaluated under the conventional banking framework, by analysing accounting statements and financial projections. The social aspects try to quantify the loan impact on the achievement of Millennium Development Goals such as employment, education, environment, health or community impact. The social credit score model should incorporate the lender's know-how and should also be coherent with its mission. This is done by using the Analytic Hierarchy Process (AHP) technique. The paper illustrates a real case: a loan application by a social enterprise presented to a socially responsible lender. The decision support system not only produces a score, but also reveals strengths and weaknesses of the application. AbstractEthical banking, microfinance institutions or certain credit cooperatives, among others, grant socially responsible loans. This paper presents a credit score system for them. The model evaluates both social and financial aspects of the borrower. The financial aspects are evaluated under the conventional banking framework, by analysing accounting statements and financial projections. The social aspects try to quantify the loan impact on the achievement of Millennium Development Goals such as employment, education, environment, health or community impact. The social credit score model should incorporate the lender's know-how and should also be coherent with its mission. This is done by using the Analytic Hierarchy Process (AHP) technique. The paper illustrates a real case: a loan application by a social enterprise presented to a socially responsible lender. The decision support system not only produces a score, but also reveals strengths and weaknesses of the application.

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“…Here we assumed that all members of the group have the same importance. However, when the individuals have different importance, [1] extended the foregoing [2] result.…”

Section: Theorem the Geometric Mean Aggregation Procedures F : P M → Pmentioning

confidence: 77%

“…The first is by [2] which proves that the geometric mean is the way to combine individual judgments into a group judgment. The second is by [1] about how to combine the judgments of judges, who have different expertise, and thus whose judgments have different priority, and the third and more recent is by [5].…”

Section: Aggregating the Judgments Of The Individuals In A Groupmentioning

confidence: 96%

How Many Judges Should There Be in a Group ?

2014

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This paper briefly examines the question of how many judges are needed to obtain valid and consistent judgments when using the analytic hierarchy process. It turns out that if a judge is experienced and well versed in an area, he can be sufficient to provide the judgments instead of diluting his accuracy with the participation of others who may not be as good. How to discover such a person requires criteria used to judge his adequacy and that of others.

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Procedures for synthesizing ratio judgements

Cited by 712 publications

References 4 publications

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

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

A Credit Score System for Socially Responsible Lending

How Many Judges Should There Be in a Group ?

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