Normalisation and rank reversals in the additive analytic hierarchy process: a new analysis

Zahir, Sajjad

doi:10.1504/ijor.2009.023538

Cited by 24 publications

(27 citation statements)

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“…Perhaps, the formula was introduced as a simple extension of the expected value formula with the normalised weights replacing probabilities. The earlier work [7] also started with the WSM and modified it to incorporate norms of the priority vectors. The new contributions in this paper include a formal mathematical derivation of the modified weighted sum method showing how the norms of priority vectors naturally appear in formal mathematics spanning the criteria and alternative spaces.…”

Section: Representation Of the Generalised Decision Space And Formulamentioning

confidence: 99%

“…The MAR was proposed as the correct aggregation procedure for obtaining overall priorities in [7]. It is worth pointing out at this stage that if the weight vector was not normalised (i.e., if in Equation (6) we used un-normalised weights W p ), we would have …”

Section: mentioning

confidence: 99%

“…Two recursion rules used in [7] for the rank reversal analysis are re-stated below (can be derived easily following the same procedure with a slight change in notations). 1) When a new alternative (i.e., the (n + 1) th alternative) is added to the decision space (the primed items refer to the corresponding quantities in the new decision space with n + 1 alternatives), in a fully consistent case,…”

Section: Recursion Rulesmentioning

confidence: 99%

“…Aggregation method b) ignores this fact causing unwanted rank reversals. Therefore, Zahir [7] suggested a modified weighted aggregation formula (based on intuitive reasoning) that incorporated norms of the priority vectors. This procedure takes into account the variation of the unit of scale across the criteria.…”

Section: Introductionmentioning

confidence: 99%

“…This procedure takes into account the variation of the unit of scale across the criteria. Zahir [7] used recursion rules and several numerical examples to illustrate the method for computing the correct aggregate relative priorities that are free from rank reversals. In contrast, the well-known simple weighted sum formula used with normalised priorities perhaps gives flawed results.…”

Section: Introductionmentioning

confidence: 99%

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Aggregation of Priorities in Multi-Criteria Decision Analysis (MCDA): Connecting Decision Spaces in the Cognitive Space

Zahir¹

2016

AJOR

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In Multi-Criteria Decision Analysis, the well-known weighted sum method for aggregating normalised relative priorities ignores the unit of scale that may vary across the criteria and thus causes rank reversals. A new aggregation rule that explicitly includes the norms of priority vectors is derived and shown as a remedy for it. An algorithmic procedure is presented to demonstrate how it can as well be used in the Analytic Hierarchy Process when norms of priority vectors are not readily available. Also, recursion relations connecting two decision spaces with added or deleted alternatives give an opportunity to extend the idea of connectivity to a new concept of cognitive space. Expanded analytic modelling embracing multiple decision spaces or scenarios may assist in detecting deficiencies in analytic models and also grasping the big picture in decision making.

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Section: Representation Of the Generalised Decision Space And Formulamentioning

confidence: 99%

Section: mentioning

confidence: 99%

Section: Recursion Rulesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Aggregation of Priorities in Multi-Criteria Decision Analysis (MCDA): Connecting Decision Spaces in the Cognitive Space

Zahir¹

2016

AJOR

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A Comprehensive Literature Review of the Rank Reversal Phenomenon in the Analytic Hierarchy Process

Maleki

Zahir

2012

Multi Criteria Decision Anal

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During the last few decades, several multi‐criteria decision analysis methods have been proposed to help in selecting the best compromise alternatives. Among them, analytic hierarchy process (AHP) and its applications have attracted much attention from academics and practitioners. However, since the early 1980s, critics have raised questions regarding its proper use. One of them concerns the unacceptable changes in the ranks of the alternatives, called rank reversal, upon changing the structure of the decision. Several modifications were suggested to preserve ranks. In this paper, a classification scheme and a comprehensive literature review are presented in order to uncover, classify and interpret the current research on AHP methodologies and rank reversals. On the basis of the scheme, 61 scholarly papers from 18 journals are categorized into specific areas. The specific areas include the papers on the topics of adding/deleting alternatives and the papers published in adding/deleting criteria. The scholarly papers are also classified by (1) year of publication, (2) journal of publication, (3) authors' geographic location and (4) using the AHP in association with other methods. It is hoped that the paper can meet the needs of researchers and practitioners for convenient references of AHP methodologies and rank reversals and hence promote the future of rank reversal research. Copyright © 2012 John Wiley & Sons, Ltd.

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Multi‐Criteria Ratios: What is the Unit?

Wedley

Choo

2011

Multi Criteria Decision Anal

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When Analytic Hierarchy Process ratios are normalized to sum to unity, the unit of measure becomes obscure. This paper investigates this obscurity and whether ratio measurement is possible when there is no prior knowledge of the measurement unit. Initially, we look at ratio scales of tangible attributes of objects with well-known measures. Then, ratio scales of unknown intangible attributes of objects are analysed. We discover that natural zero and a specific unit of measure are not necessarily used explicitly in deriving ratio scale measures. Nevertheless, the derived scale does have a derived unit of measurement. We conclude that although composite multi-criteria answers are possible in ratio form, it is important to know that a unit of measure exists if ambiguities are to be avoided.

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Normalisation and rank reversals in the additive analytic hierarchy process: a new analysis

Cited by 24 publications

References 0 publications

Aggregation of Priorities in Multi-Criteria Decision Analysis (MCDA): Connecting Decision Spaces in the Cognitive Space

Aggregation of Priorities in Multi-Criteria Decision Analysis (MCDA): Connecting Decision Spaces in the Cognitive Space

A Comprehensive Literature Review of the Rank Reversal Phenomenon in the Analytic Hierarchy Process

Multi‐Criteria Ratios: What is the Unit?

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