Interval weight generation approaches based on consistency test and interval comparison matrices

Ying Ming Wang; Jian Bo Yang; Dong Ling Xu

doi:10.1016/j.amc.2004.06.080

Interval weight generation approaches based on consistency test and interval comparison matrices

Ying Ming Wang, Jian Bo Yang, Dong Ling Xu

Research output: Contribution to journal › Article › peer-review

Abstract

A simple yet pragmatic method of consistency test is developed to check whether an interval comparison matrix is consistent or not. Linear programming method is used to derive consistent interval weights from consistent interval comparison matrices and to aggregate local interval weights to generate global interval weights. In cases where an interval comparison matrix is inconsistent, an eigenvector method-based nonlinear programming (NLP) approach is developed to generate interval weights that can meet pre-determined consistency requirements. A simple and effective preference ranking method is utilized to compare the interval weights of criteria or rank alternatives. Three numerical examples including a hierarchical (AHP) decision problem are provided to illustrate the validity and practicality of the proposed methods. © 2004 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	252-273
Number of pages	21
Journal	Applied Mathematics and Computation
Volume	167
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2004.06.080
Publication status	Published - 5 Aug 2005

Keywords

Analytic hierarchy process
Consistency test
Interval comparison matrix
Linear and nonlinear programming
Preference ranking
Weight estimation

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10.1016/j.amc.2004.06.080

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title = "Interval weight generation approaches based on consistency test and interval comparison matrices",

abstract = "A simple yet pragmatic method of consistency test is developed to check whether an interval comparison matrix is consistent or not. Linear programming method is used to derive consistent interval weights from consistent interval comparison matrices and to aggregate local interval weights to generate global interval weights. In cases where an interval comparison matrix is inconsistent, an eigenvector method-based nonlinear programming (NLP) approach is developed to generate interval weights that can meet pre-determined consistency requirements. A simple and effective preference ranking method is utilized to compare the interval weights of criteria or rank alternatives. Three numerical examples including a hierarchical (AHP) decision problem are provided to illustrate the validity and practicality of the proposed methods. {\textcopyright} 2004 Elsevier Inc. All rights reserved.",

keywords = "Analytic hierarchy process, Consistency test, Interval comparison matrix, Linear and nonlinear programming, Preference ranking, Weight estimation",

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AU - Xu, Dong Ling

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N2 - A simple yet pragmatic method of consistency test is developed to check whether an interval comparison matrix is consistent or not. Linear programming method is used to derive consistent interval weights from consistent interval comparison matrices and to aggregate local interval weights to generate global interval weights. In cases where an interval comparison matrix is inconsistent, an eigenvector method-based nonlinear programming (NLP) approach is developed to generate interval weights that can meet pre-determined consistency requirements. A simple and effective preference ranking method is utilized to compare the interval weights of criteria or rank alternatives. Three numerical examples including a hierarchical (AHP) decision problem are provided to illustrate the validity and practicality of the proposed methods. © 2004 Elsevier Inc. All rights reserved.

AB - A simple yet pragmatic method of consistency test is developed to check whether an interval comparison matrix is consistent or not. Linear programming method is used to derive consistent interval weights from consistent interval comparison matrices and to aggregate local interval weights to generate global interval weights. In cases where an interval comparison matrix is inconsistent, an eigenvector method-based nonlinear programming (NLP) approach is developed to generate interval weights that can meet pre-determined consistency requirements. A simple and effective preference ranking method is utilized to compare the interval weights of criteria or rank alternatives. Three numerical examples including a hierarchical (AHP) decision problem are provided to illustrate the validity and practicality of the proposed methods. © 2004 Elsevier Inc. All rights reserved.

KW - Analytic hierarchy process

KW - Consistency test

KW - Interval comparison matrix

KW - Linear and nonlinear programming

KW - Preference ranking

KW - Weight estimation

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DO - 10.1016/j.amc.2004.06.080

M3 - Article

SN - 0096-3003

VL - 167

SP - 252

EP - 273

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 1

ER -

Interval weight generation approaches based on consistency test and interval comparison matrices

Abstract

Keywords

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