Notes on order preservation and consistency in AHP

Kułakowski, Konrad

doi:10.1016/j.ejor.2015.03.010

Cited by 62 publications

(29 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Usually, the PC method is used with a multiplicative PC matrix, i.e., with multiplicative alo-group, see e.g. [30,24]. Then the relative importance of an alternative is multiplied with the relative importance of the other alternatives when considering a chain of alternatives.…”

Section: Preliminaries Pairwise Comparisons Methodsmentioning

confidence: 99%

When is the condition of order preservation met?

Kułakowski

Mazurek

Ramík

et al. 2019

European Journal of Operational Research

Self Cite

View full text Add to dashboard Cite

This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group is investigated. This approach allows for a generalization of previous results. Sufficient conditions for order preservation based on the properties of elements of pairwise comparisons matrix are derived. A numerical example is presented.

show abstract

Section: Preliminaries Pairwise Comparisons Methodsmentioning

confidence: 99%

When is the condition of order preservation met?

Kułakowski

Mazurek

Ramík

et al. 2019

European Journal of Operational Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…where • denotes the Frobenius norm. Kułakowski (2015) considered the condition of order preservation (COP) proposed by Bana e Costa and Vansnick (2008) and suggested the following inconsistency index…”

Section: Ati(a)mentioning

confidence: 99%

A survey of inconsistency indices for pairwise comparisons

Brunelli

2018

International Journal of General Systems

104

View full text Add to dashboard Cite

Pairwise comparisons are a well-established tool to compare weights of criteria and alternatives or, more in general, any entities. Their ultimate goal is to facilitate the search for a suitable weight vector. In this context, the concepts of inconsistency and inconsistency index have emerged. This manuscript has two goals. Firstly, it surveys the most relevant inconsistency indices by means of a self-contained exposition. Secondly, by analyzing recent trends and milestones it presents some conclusions and a discussion on possible directions of future research.

show abstract

“…Different thresholds have been proposed for checking acceptable consistency (Aguaron & Moreno-Jimenez, 2003). Despite the fact that Saaty's CR has been criticized for yielding unreasonable consistency result with respect to the condition of order preservation (Bana e Costa & Vansnick, 2008;Kułakowski, 2015), it remains the most widely used acceptable consistency in literature (Ishizaka & Labib, 2011).…”

Section: New Acceptable Consistency and Acceptability Of Imcmsmentioning

confidence: 99%

Acceptability analysis and priority weight elicitation for interval multiplicative comparison matrices

Wang

Tong

2016

European Journal of Operational Research

View full text Add to dashboard Cite

Existing research on acceptability of pairwise interval comparison matrices focuses on acceptable consistency by controlling their inconsistency levels to within a certain threshold. However, a perfectly consistent but highly indeterminate interval comparison matrix can be unacceptable as it contains little (sometimes no) useful decision information. This paper first analyzes the current definition of acceptable consistency for interval multiplicative comparison matrices (IMCMs) and shows its technical deficiencies. We then introduce a new notion of acceptable IMCMs, considering both inconsistency and indeterminacy levels in IMCMs. A geometric-mean-based index is proposed to measure the indeterminacy ratio of an IMCM, and useful properties are derived for consistent IMCMs and acceptable IMCMs. An indeterminacyratio and geometric-mean-based transformation equation is subsequently put forward to convert normalized acceptable interval multiplicative weights into an acceptable IMCM with consistency. By introducing an auxiliary constraint, a logarithmic least square model is established to generate interval multiplicative weights from acceptable IMCMs. A geometricmean-based possibility degree formula is designed to compare and rank normalized interval multiplicative weights. Two numerical examples are presented to illustrate how to utilize the proposed framework.

show abstract

Notes on order preservation and consistency in AHP

Cited by 62 publications

References 25 publications

When is the condition of order preservation met?

When is the condition of order preservation met?

A survey of inconsistency indices for pairwise comparisons

Acceptability analysis and priority weight elicitation for interval multiplicative comparison matrices

Contact Info

Product

Resources

About