Incomplete pairwise comparative judgments: Recent developments and a proposed method

Alrasheedi, Melfi

doi:10.5267/j.dsl.2019.1.002

Cited by 7 publications

(4 citation statements)

References 30 publications

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“…Here, we use a simple coordinate transformation technique [38] (pp. [23][24]; [34,36] evolved from a trigonometric function sin(z) for dual bound constraints (lower and upper bounds).…”

Section: The Coordinate Transformation Methodsmentioning

confidence: 99%

“…Kułakowski [22] extended the geometric mean method (GMM) for an incomplete PCM, leading to the same results obtained using the logarithmic least square method (LLSM) for incomplete PCM by Bozóki et al [15], where the weight ratio w i /w j substitutes the missing comparisons in the incomplete PCM. In addition, other researchers have studied several completion methods for incomplete PCMs [23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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Constrained Eigenvalue Minimization of Incomplete Pairwise Comparison Matrices by Nelder-Mead Algorithm

2021

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Pairwise comparison matrices play a prominent role in multiple-criteria decision-making, particularly in the analytic hierarchy process (AHP). Another form of preference modeling, called an incomplete pairwise comparison matrix, is considered when one or more elements are missing. In this paper, an algorithm is proposed for the optimal completion of an incomplete matrix. Our intention is to numerically minimize a maximum eigenvalue function, which is difficult to write explicitly in terms of variables, subject to interval constraints. Numerical simulations are carried out in order to examine the performance of the algorithm. The results of our simulations show that the proposed algorithm has the ability to solve the minimization of the constrained eigenvalue problem. We provided illustrative examples to show the simplex procedures obtained by the proposed algorithm, and how well it fills in the given incomplete matrices.

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“…Here, we use a simple coordinate transformation technique [38] (pp. [23][24]; [34,36] evolved from a trigonometric function sin(z) for dual bound constraints (lower and upper bounds).…”

Section: The Coordinate Transformation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Constrained Eigenvalue Minimization of Incomplete Pairwise Comparison Matrices by Nelder-Mead Algorithm

2021

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“…Na ilustração do problema de aquisição de aeronaves de ataque, com a estrutura de 6 critérios (Figura 1), o modelo simplificado proposto por Gavião, Lima e Garcia (2021) exigiria do avaliador apenas cinco julgamentos para esse nível, ao invés de 15 previstos no modelo original do AHP. Este artigo não aprofunda esses procedimentos de simplificação da coleta de dados do AHP, porém é possível encontrar diferentes soluções na literatura (ÁGOSTON;CSATÓ, 2022;ALRASHEEDI, 2019;GARCIA, 2021;LEAL, 2020;ZHOU et al, 2018).…”

Section: Metodologia De Cálculo Do Ahpunclassified

O apoio à decisão em aquisição de defesa: estruturando problemas multicritérios com o Processo de Análise Hierárquica (AHP)

Gaviao,

Kostin

2023

cmm

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A aquisição de produtos, sistemas ou componentes de sistemas de defesa possui características que tornam a Pesquisa Operacional especialmente útil para problemas de escolha de material para as Forças Armadas, incluindo a teoria de apoio à decisão multicritério. O problema de aquisição de defesa se adequa a essa metodologia pois envolve o uso de critérios de decisão para a escolha mais satisfatória entre um conjunto finito de produtos de defesa, pois a alta tecnologia e os vultosos recursos exigidos para a produção desses sistemas torna o mercado de defesa restrito a poucos desenvolvedores e fabricantes. Um método multicritério com amplo uso na indústria de defesa é o Processo de Análise Hierárquica (AHP), por sua simplicidade, lógica e possibilidade de validação das avaliações de especialistas. As equações de cálculo do AHP são aqui descritas e podem ser implementadas em diferentes softwares, que incluem o Excel, o R, Python, entre outros. Uma aplicação simulada apresentou a forma de coleta de dados e a sequência de cálculos do AHP para um problema de escolha de três aeronaves, avaliadas sob seis critérios, indicando a ordem de preferência de um especialista.

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“…Zhou et al [43] proposed a DEMATEL-based completion method for incomplete PC matrices. Different priority deriving methods for incomplete PC matrices can also be found in Alrasheedi [44]. The problem of inconsistent, incomplete PC matrices has also been discussed by several researchers [30,45,46].…”

Section: Introductionmentioning

confidence: 99%

On the Geometric Mean Method for Incomplete Pairwise Comparisons

Kułakowski

2020

Mathematics

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One of the most popular methods of calculating priorities based on the pairwise comparisons matrices (PCM) is the geometric mean method (GMM). It is equivalent to the logarithmic least squares method (LLSM), so some use both names interchangeably, treating it as the same approach. The main difference, however, is in the way the calculations are done. It turns out, however, that a similar relationship holds for incomplete matrices. Based on Harker’s method for the incomplete PCM, and using the same substitution for the missing entries, it is possible to construct the geometric mean solution for the incomplete PCM, which is fully compatible with the existing LLSM for the incomplete PCM. Again, both approaches lead to the same results, but the difference is how the final solution is computed. The aim of this work is to present in a concise form, the computational method behind the geometric mean method (GMM) for an incomplete PCM. The computational method is presented to emphasize the relationship between the original GMM and the proposed solution. Hence, everyone who knows the GMM for a complete PCM should easily understand its proposed extension. Theoretical considerations are accompanied by a numerical example, allowing the reader to follow the calculations step by step.

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Incomplete pairwise comparative judgments: Recent developments and a proposed method

Cited by 7 publications

References 30 publications

Constrained Eigenvalue Minimization of Incomplete Pairwise Comparison Matrices by Nelder-Mead Algorithm

Constrained Eigenvalue Minimization of Incomplete Pairwise Comparison Matrices by Nelder-Mead Algorithm

O apoio à decisão em aquisição de defesa: estruturando problemas multicritérios com o Processo de Análise Hierárquica (AHP)

On the Geometric Mean Method for Incomplete Pairwise Comparisons

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