A new measure of consistency for positive reciprocal matrices

Peláez, José Ignacio; Lamata, María Teresa

doi:10.1016/s0898-1221(03)90240-9

Cited by 142 publications

(70 citation statements)

References 4 publications

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“…According to our tests, even a small inconsistency in just one of the comparisons could increase the CR above the threshold of 0.1. Similar problems are reported in ratio-scale pairwise comparisons based on other types of surveys (Sironen et al 2013), and other measures have been presented for evaluating the inconsistencies (Peláez and Lamata 2003;Ramík and Korviny 2010) and uncertainties related to the process overall (see Alho and Kangas 1997), differing from those originally proposed by Saaty (1980). According to the earlier studies on the preferences on forest use, the majority of citizens, regardless of forest ownership, do not approve of clearcutting (Valkeapää and Karppinen 2013).…”

Section: Discussionmentioning

confidence: 53%

Reconstructing forest canopy from the 3D triangulations of airborne laser scanning point data for the visualization and planning of forested landscapes

Ruotsalainen

2017

Annals of Forest Science

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& Key messageWe present a data-driven technique to visualize forest landscapes and simulate their future development according to alternative management scenarios. Gentle harvesting intensities were preferred for maintaining scenic values in a test of eliciting public's preferences based on the simulated landscapes. & Context Visualizations of future forest landscapes according to alternative management scenarios are useful for eliciting stakeholders' preferences on the alternatives. However, conventional computer visualizations require laborious tree-wise measurements or simulators to generate these observations. & Aims We describe and evaluate an alternative approach, in which the visualization is based on reconstructing forest canopy from sparse density, leaf-off airborne laser scanning data. & Methods Computational geometry was employed to generate filtrations, i.e., ordered sets of simplices belonging to the three-dimensional triangulations of the point data. An appropriate degree of filtering was determined by analyzing the topological persistence of the filtrations. The topology was further utilized to simulate changes to canopy biomass, resembling harvests with varying retention levels. Relative priorities of recreational and scenic values of the harvests were estimated based on pairwise comparisons and analytic hierarchy process (AHP). & Results The canopy elements were co-located with the tree stems measured in the field, and the visualizations derived from the entire landscape showed reasonably realistic, despite a low numerical correspondence with plot-level forest attributes. The potential and limitations to improve the proposed parameterization are discussed. & Conclusion Although the criteria to evaluate the landscape visualization and simulation models were not conclusive, the results suggest that forest scenes may be feasibly reconstructed based on data already covering broad areas and readily available for practical applications.

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Section: Discussionmentioning

confidence: 53%

Reconstructing forest canopy from the 3D triangulations of airborne laser scanning point data for the visualization and planning of forested landscapes

Ruotsalainen

2017

Annals of Forest Science

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“…Many matrix consistency testing methods were developed, such as matrix determinant (Pelaez and Lamata 2003), ratio of calculated priorities and given comparison (Grawford and Williams 1985), transitivity rule (Salo and Hamalainen 1997;Ji and Jiang 2003), and normalized column of the comparison matrix (Stein and Mizzi 2007). However, Saaty's (1997) consistency ratio (CR), which uses the Eigenvalue prioritization method, is most commonly used in the literature.…”

Section: Evaluation Of Alternatives and Criteriamentioning

confidence: 99%

Analysis of MCDM methods output coherence in oil and gas portfolio prioritization

Qaradaghi

Deason

2017

J Petrol Explor Prod Technol

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This research paper aims at developing a triplex multi-criteria decision model to achieve an optimum allocation of resources to a portfolio of oilfields based on a number of criteria that pertain to the oilfields' technical and contextual characteristics. It also offers an approach for validating the prioritization results generated by the methods used through a two-dimensional test that compares the internal and external prioritization stability of three multi-criteria decision making (MCDM) methods against a conventional Intuitive approach. The MCDM methods used include Analytic Hierarchy Process (AHP), Preference Ranking Organization METHod for Enriched Evaluation (PROMETHEE), and Technique of Order Preference Similarity to the Ideal Solution (TOPSIS). The internal and external consistency testing results are outlined in nine possible scenarios through which a conclusion is derived confirming the competitive advantage of MCDM methods.

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“…2,6,7 The consistency index CI has been questioned because it is not easy to compute, has not a simple and geometric meaning 8,9 and, in some cases, seems to be unfair. 10 Also, the methods used to provide a weighted ranking have been questioned: indeed they may indicate rankings that do not agree with the expressed preference ratios a ij .…”

Section: N (Additive Consistency)mentioning

confidence: 99%

A general unified framework for pairwise comparison matrices in multicriterial methods

Cavallo

D’Apuzzo

2009

Int. J. Intell. Syst.

119

112

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In a Multicriteria Decision Making context, a pairwise comparison matrix $A=(a_{ij})$ is a helpful tool to determine the weighted ranking on a set $X$ of alternatives or criteria. The entry $a_{ij}$ of the matrix can assume different meanings: $a_{ij}$ can be a preference ratio (multiplicative case) or a preference difference (additive case) or $a_{ij}$ belongs to $[0,1]$ and measures the distance from the indifference that is expressed by 0.5 (fuzzy case). For the multiplicative case, a consistency index for the matrix $A$ has been provided by T.L. Saaty in terms of maximum eigenvalue. We consider pairwise comparison matrices over an abelian linearly ordered group and, in this way, we provide a general framework including the mentioned cases. By introducing a more general notion of metric, we provide a consistency index that has a natural meaning and it is easy to compute in the additive and multiplicative cases; in the other cases, it can be computed easily starting from a suitable additive or multiplicative matrix

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A new measure of consistency for positive reciprocal matrices

Cited by 142 publications

References 4 publications

Reconstructing forest canopy from the 3D triangulations of airborne laser scanning point data for the visualization and planning of forested landscapes

Reconstructing forest canopy from the 3D triangulations of airborne laser scanning point data for the visualization and planning of forested landscapes

Analysis of MCDM methods output coherence in oil and gas portfolio prioritization

A general unified framework for pairwise comparison matrices in multicriterial methods

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