# A Statistical Hypothesis Testing Method for the Rank Ordering of the Priorities of the Alternatives in the Analytic Hierarchy Process

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

In analytic hierarchy process (AHP), a ratio scale (π12,...,πt) for the priorities of the alternatives {T1,T2,...,Tt} is used for a decision problem in which πij is used to quantify the ratio of the priority of Ti to that of Tj. In a group decision-making setup, the subjective estimates of πij are obtained as entries of a pairwise comparison matrix for each member of the group. On the basis of these pairwise comparison matrices, one of the topics of interest in some situation is the total rank ordering of the priorities of the alternatives. In this article, a statistical method is proposed for testing a specific total rank ordering of the priorities of the alternatives. The method developed is then illustrated using numerical examples.

Original language English (US) 161-166 6 Journal of Multi-Criteria Decision Analysis 22 3-4 https://doi.org/10.1002/mcda.1526 Published - May 1 2015

### Fingerprint

Analytic hierarchy process
Hypothesis testing
Pairwise comparisons
Statistical methods
Group decision making
Testing

### All Science Journal Classification (ASJC) codes

• Decision Sciences(all)
• Strategy and Management

### Cite this

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title = "A Statistical Hypothesis Testing Method for the Rank Ordering of the Priorities of the Alternatives in the Analytic Hierarchy Process",
abstract = "In analytic hierarchy process (AHP), a ratio scale (π1,π2,...,πt) for the priorities of the alternatives {T1,T2,...,Tt} is used for a decision problem in which πi/πj is used to quantify the ratio of the priority of Ti to that of Tj. In a group decision-making setup, the subjective estimates of πi/πj are obtained as entries of a pairwise comparison matrix for each member of the group. On the basis of these pairwise comparison matrices, one of the topics of interest in some situation is the total rank ordering of the priorities of the alternatives. In this article, a statistical method is proposed for testing a specific total rank ordering of the priorities of the alternatives. The method developed is then illustrated using numerical examples.",
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day = "1",
doi = "10.1002/mcda.1526",
language = "English (US)",
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journal = "Journal of Multi-Criteria Decision Analysis",
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publisher = "John Wiley and Sons Ltd",
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In: Journal of Multi-Criteria Decision Analysis, Vol. 22, No. 3-4, 01.05.2015, p. 161-166.

Research output: Contribution to journalArticle

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AB - In analytic hierarchy process (AHP), a ratio scale (π1,π2,...,πt) for the priorities of the alternatives {T1,T2,...,Tt} is used for a decision problem in which πi/πj is used to quantify the ratio of the priority of Ti to that of Tj. In a group decision-making setup, the subjective estimates of πi/πj are obtained as entries of a pairwise comparison matrix for each member of the group. On the basis of these pairwise comparison matrices, one of the topics of interest in some situation is the total rank ordering of the priorities of the alternatives. In this article, a statistical method is proposed for testing a specific total rank ordering of the priorities of the alternatives. The method developed is then illustrated using numerical examples.

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