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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Vydáno v:	Mathematical and computer modelling Ročník 54; číslo 11; s. 2736 - 2749
Hlavní autoři:	Huo, Liang-an, Lan, Jibin, Wang, Zhongxing
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Kidlington Elsevier Ltd 01.12.2011 Elsevier
Témata:	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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Abstract	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.
AbstractList	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. 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.
Author	Lan, Jibin Wang, Zhongxing Huo, Liang-an
Author_xml	– sequence: 1 givenname: Liang-an surname: Huo fullname: Huo, Liang-an organization: Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052, PR China – sequence: 2 givenname: Jibin surname: Lan fullname: Lan, Jibin email: huohuolin@hotmail.com organization: School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, PR China – sequence: 3 givenname: Zhongxing surname: Wang fullname: Wang, Zhongxing organization: School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, PR China
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Keywords	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
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Snippet	In this paper, new parametric prioritization methods (PPMs) to determine a family of priority vectors in an analytical hierarchy process (AHP) are proposed,...
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SubjectTerms	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
Title	New parametric prioritization methods for an analytical hierarchy process based on a pairwise comparison matrix
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