Effectiveness Analysis of Deriving Priority Vectors From Reciprocal Pairwise Comparison Matrices

Bajwa, Gurjit S.; Choo, Eng Ung; Wedley, William C.

doi:10.1142/s0217595908001754

Cited by 36 publications

(37 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…One of these efficiency conditions is utilized in our paper, which applies a directed graph representation. [1] and by Conde and Pérez [7] and also by Fedrizzi [12].…”

Section: Definition 1 a Positive Weight Vector W Is Called Efficientmentioning

confidence: 99%

“…Being an economist, engineer, decision theorist, preference modeler or mathematician, who faces an estimation problem, inefficient solutions are hard to argue for. The comparative studies of weighting methods, such as [1,6,9,13], should be extended by adding efficiency to the list of axioms/criteria.…”

Section: Conclusion and Open Questionsmentioning

confidence: 99%

“…, n. The column vector w is usually normalized so that i w i = 1. A weight vector can be extracted from a PCM in several ways [1,6,9,13], however, the paper investigates the eigenvector method [14] only. If A is consistent, then the eigenvector equation Aw = nw holds, and w i /w j = a ij , i, j = 1, 2, .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficiency Analysis of Simple Perturbed Pairwise Comparison Matrices

Ábele-Nagy

Bozóki

Rebák

2016

View full text Add to dashboard Cite

Efficiency, the basic concept of multi-objective optimization is investigated for the class of pairwise comparison matrices. A weight vector is called efficient if no alternative weight vector exists such that every pairwise ratio of the latter's components is at least as close to the corresponding element of the pairwise comparison matrix as the one of the former's components is, and the latter's approximation is strictly better in at least one position. A pairwise comparison matrix is called simple perturbed if it differs from a consistent pairwise comparison matrix in one element and its reciprocal. One of the classical weighting methods, the eigenvector method is analyzed. It is shown in the paper that the principal right eigenvector of a simple perturbed pairwise comparison matrix is efficient. An open problem is exposed: the search for a necessary and sufficient condition of that the principal right eigenvector is efficient.

show abstract

“…One of these efficiency conditions is utilized in our paper, which applies a directed graph representation. [1] and by Conde and Pérez [7] and also by Fedrizzi [12].…”

Section: Definition 1 a Positive Weight Vector W Is Called Efficientmentioning

confidence: 99%

Section: Conclusion and Open Questionsmentioning

confidence: 99%

See 1 more Smart Citation

Efficiency Analysis of Simple Perturbed Pairwise Comparison Matrices

Ábele-Nagy

Bozóki

Rebák

2016

View full text Add to dashboard Cite

show abstract

“…Local preferences are assumed to be measured in ordinal scale in ranking models [6], in interval scale in multiple attribute utility models [7] and in ratio scale in AHP type models [8,9]. There are many methods proposed for deriving local preferences from pairwise comparison matrices [4,5,[13][14][15][16]. The local preference vectors x 1 ,x 2 ,…,x m and the criteria weight vector w are then aggregated into overall preference vector v=[v 1 ,v 2 ,…,v n ] by the additive aggregation [9,17] or the multiplicative aggregation [2].…”

Section: Literature Reviewmentioning

confidence: 99%

“…Goal programming and data development analysis are also used in some MCDM models [14,16,18,19]. Most of these methods have been extensively analyzed and compared [1,4,5,15,20].…”

Section: Literature Reviewmentioning

confidence: 99%

Comparing Fundamentals of Additive and Multiplicative Aggregation in Ratio Scale Multi-Criteria Decision Making

Choo¹,

Wedley²

2008

TOORJ

Self Cite

View full text Add to dashboard Cite

Additive and multiplicative aggregations of ratio scale preferences are frequently used in multi-criteria decision making models. In this paper, we compare the advantages and limitations of these two aggregation rules by exploring only their fundamental properties after ratio scaled local priorities and criteria weights have been successfully generated from the decision maker. The comparisons of these properties are therefore independent of ancillary procedures such as interactive elicitations from decision makers, pairwise comparisons and calculations of local priorities and criteria weights. We compare six fundamental properties of the two aggregation rules. The criteria weights used in the multiplicative aggregation have complicated meanings which are not well understood and often mixed up in the ambiguous notion of "criteria importance". As the scaling factors of the local preference values do not appear explicitly in the computations of the relative ratios of the overall preferences in the multiplicative aggregation model, the relative ratios remain unchanged when the scaling factors are changed or an alternative is added or deleted. Furthermore, the relative ratios in the multiplicative aggregation do not depend on similar local preference values which cancel each other out mathematically. It is quite evident that the additive aggregation model is superior and easier for decision makers to use and understand. We recommend the additive aggregation rule over the multiplicative aggregation rule.

show abstract

Sharing the pie and distributing the reward: a case of bonus distribution among executives

Wedley

Choo

2008

Multi Criteria Decision Anal

Self Cite

View full text Add to dashboard Cite

Relevant criteria can be identified and used to partition and disaggregate a project's overall impact value into separate components to be evaluated independently under each criterion. Criteria weights can then be used to distribute the benefit of the joint project to its contributors. There are different interpretations of the criteria weights in different methods of benefit sharing. Project team members are motivated by the distribution of benefits. Criteria weights with different interpretations can be used as part of management incentives in setting up the joint project. In this work, different AHP type models are analyzed for a hypothetical case of bonus distribution to key executives. The implications of appropriate interpretations of criteria weights and local priorities are examined. Other sharing methods are discussed and analyzed. The method of bonus sharing based on the overall priorities of the contributions of all contributors is shown to produce resulting bonus shares that are always proportional to the actual contributions of the executives in the sharing set.

show abstract

Effectiveness Analysis of Deriving Priority Vectors From Reciprocal Pairwise Comparison Matrices

Cited by 36 publications

References 30 publications

Efficiency Analysis of Simple Perturbed Pairwise Comparison Matrices

Efficiency Analysis of Simple Perturbed Pairwise Comparison Matrices

Comparing Fundamentals of Additive and Multiplicative Aggregation in Ratio Scale Multi-Criteria Decision Making

Sharing the pie and distributing the reward: a case of bonus distribution among executives

Contact Info

Product

Resources

About