New parametric prioritization methods for an analytical hierarchy process based on a pairwise comparison matrix

In this paper, new parametric prioritization methods (PPMs) to determine a family of priority vectors in an analytical hierarchy process (AHP) are proposed, pointing out the logical relation of elements in the comparative matrix. The scales and consistency cannot determine the priorities, but only t...

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Veröffentlicht in:Mathematical and computer modelling Jg. 54; H. 11; S. 2736 - 2749
Hauptverfasser: Huo, Liang-an, Lan, Jibin, Wang, Zhongxing
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Kidlington Elsevier Ltd 01.12.2011
Elsevier
Schlagworte:
Analytic hierarchy process (AHP)
analytical methods
cognition
Consistency
Exact sciences and technology
Judgment matrix
Logic and foundations
Mathematical analysis
Mathematical logic, foundations, set theory
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming
Numerical methods in mathematical programming, optimization and calculus of variations
Parametric prioritization method (PPM)
prioritization
Priority
Recursion theory
Sciences and techniques of general use
Analytic hierarchy process (AHP)
Judgment matrix
Parametric prioritization method (PPM)
Priority
Consistency
Mathematical series
Optimization method
Analytic hierarchy process
Numerical analysis
Applied mathematics
Analytical method
Mathematical model
Computer aided analysis
Mathematical programming
ISSN:0895-7177, 1872-9479
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Zusammenfassung:In this paper, new parametric prioritization methods (PPMs) to determine a family of priority vectors in an analytical hierarchy process (AHP) are proposed, pointing out the logical relation of elements in the comparative matrix. The scales and consistency cannot determine the priorities, but only the order of the alternatives. To derive the priorities of alternatives, a series of theorems and mathematical programming models is given based on a pairwise comparison matrix. This refers to parameters θ , α , β , by which there exists a family of priorities for the same judgment matrix. The discrimination of alternatives can be easily improved when using the proposed priority method by modifying the values of the parameters. Some false cognitions about how to determine the priority of an analytical hierarchy process are rectified. One should not elicit priority vectors from the judgment matrix; the information is incomplete, and the parameters must be considered. Finally, the meanings of parameters are explained in practical applications and an approach for determining the values of the parameters is proposed. Examples are also used to illustrate the features and applicability of the new approach in an AHP.
Bibliographie:ObjectType-Article-1
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ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2011.06.062