A goal programming method for obtaining interval weights from an interval comparison matrix

Ying Ming Wang; T. M S Elhag

doi:10.1016/j.ejor.2005.10.066

A goal programming method for obtaining interval weights from an interval comparison matrix

Ying Ming Wang, T. M S Elhag

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

Abstract

Crisp comparison matrices lead to crisp weight vectors being generated. Accordingly, an interval comparison matrix should give an interval weight estimate. In this paper, a goal programming (GP) method is proposed to obtain interval weights from an interval comparison matrix, which can be either consistent or inconsistent. The interval weights are assumed to be normalized and can be derived from a GP model at a time. The proposed GP method is also applicable to crisp comparison matrices. Comparisons with an interval regression analysis method are also made. Three numerical examples including a multiple criteria decision-making (MCDM) problem with a hierarchical structure are examined to show the potential applications of the proposed GP method. © 2006 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	458-471
Number of pages	13
Journal	European Journal of Operational Research
Volume	177
Issue number	1
DOIs	https://doi.org/10.1016/j.ejor.2005.10.066
Publication status	Published - 16 Feb 2007

Keywords

Analytic hierarchy process
Interval comparison matrix
Interval regression analysis
Multiple criteria decision making
Normalization

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10.1016/j.ejor.2005.10.066

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title = "A goal programming method for obtaining interval weights from an interval comparison matrix",

abstract = "Crisp comparison matrices lead to crisp weight vectors being generated. Accordingly, an interval comparison matrix should give an interval weight estimate. In this paper, a goal programming (GP) method is proposed to obtain interval weights from an interval comparison matrix, which can be either consistent or inconsistent. The interval weights are assumed to be normalized and can be derived from a GP model at a time. The proposed GP method is also applicable to crisp comparison matrices. Comparisons with an interval regression analysis method are also made. Three numerical examples including a multiple criteria decision-making (MCDM) problem with a hierarchical structure are examined to show the potential applications of the proposed GP method. {\textcopyright} 2006 Elsevier B.V. All rights reserved.",

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AU - Elhag, T. M S

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N2 - Crisp comparison matrices lead to crisp weight vectors being generated. Accordingly, an interval comparison matrix should give an interval weight estimate. In this paper, a goal programming (GP) method is proposed to obtain interval weights from an interval comparison matrix, which can be either consistent or inconsistent. The interval weights are assumed to be normalized and can be derived from a GP model at a time. The proposed GP method is also applicable to crisp comparison matrices. Comparisons with an interval regression analysis method are also made. Three numerical examples including a multiple criteria decision-making (MCDM) problem with a hierarchical structure are examined to show the potential applications of the proposed GP method. © 2006 Elsevier B.V. All rights reserved.

AB - Crisp comparison matrices lead to crisp weight vectors being generated. Accordingly, an interval comparison matrix should give an interval weight estimate. In this paper, a goal programming (GP) method is proposed to obtain interval weights from an interval comparison matrix, which can be either consistent or inconsistent. The interval weights are assumed to be normalized and can be derived from a GP model at a time. The proposed GP method is also applicable to crisp comparison matrices. Comparisons with an interval regression analysis method are also made. Three numerical examples including a multiple criteria decision-making (MCDM) problem with a hierarchical structure are examined to show the potential applications of the proposed GP method. © 2006 Elsevier B.V. All rights reserved.

KW - Analytic hierarchy process

KW - Interval comparison matrix

KW - Interval regression analysis

KW - Multiple criteria decision making

KW - Normalization

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DO - 10.1016/j.ejor.2005.10.066

M3 - Article

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SP - 458

EP - 471

JO - European Journal of Operational Research

JF - European Journal of Operational Research

IS - 1

ER -

A goal programming method for obtaining interval weights from an interval comparison matrix

Abstract

Keywords

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