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

@article{Saaty2008RelativeMA,
  title={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},
  author={Thomas L. Saaty},
  journal={RACSAM - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas},
  year={2008},
  volume={102},
  pages={251-318}
}
  • T. Saaty
  • Published 2008
  • Mathematics
  • RACSAM - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
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… Expand
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References

SHOWING 1-10 OF 29 REFERENCES
On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process
TLDR
Fuzzy set theory has serious difficulties in producing valid answers in decision-making by fuzzifying judgments, and improving the consistency of a judgment matrix does not necessarily improve the validity of the outcome. Expand
Fundamentals of Decision Making
In institutions ranging from private households, to companies, and public administration, people on whichever hierarchical level are responsible for certain domains, and thus make decisions on aExpand
Experiments on rank preservation and reversal in relative measurement
We 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, yieldExpand
Procedures for Synthesizing Ratio Judgements
Requirements which seem reasonable for functions synthesizing judgements (quantities or their ratios), in particular separability, associativity or bisymmetry, cancellativity, consensus, reciprocalExpand
On a simple linear functional equation on normed linear spaces
Summary. In the present paper, we consider the linear functional equation¶¶ $ \Phi (\alpha x) - \beta \Phi(x) = F(x) \qquad (x \in E) $,(1)¶where E and G are normed linear spaces over K, K is eitherExpand
ADDRESSING WITH BREVITY CRITICISMS OF THE ANALYTIC HIERARCHY PROCESS
The 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 toExpand
Social Choice and Individual Values.
If you want to have a destination search and find the appropriate manuals for your products, you can visit this website providing you with many Social Choice And Individual Values. You can find theExpand
On synthesis of judgements
Abstract We discuss several conditions which are reasonable to require for functions synthesizing either ratio or measure judgements, (or both) and determine all synthesizing functions satisfyingExpand
The algebraic eigenvalue problem
Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices ofExpand
Implementing neural firing: Towards a new technology
TLDR
Following earlier work on neural firing and synthesis, the expressions derived elsewhere in the literature are used to show how to represent images and sounds with the aid of CLOS (Common Lisp Object System) computer program of the LISP computer language. Expand
...
1
2
3
...