Some new properties of inconsistent pairwise comparisons matrices

Mazurek, Jiří; Ramík, Jaroslav

doi:10.1016/j.ijar.2019.07.002

Cited by 25 publications

(13 citation statements)

References 14 publications

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“…To evaluate the degree of this inconsistency, many inconsistency indices have been proposed in the literature and their properties extensively studied, see e.g. [2], [8], [9], [10], [12], [24], [28], [32], [33], [34], or [37].…”

Section: Preliminariesmentioning

confidence: 99%

A Numerical Comparison of Iterative Algorithms for Inconsistency Reduction in Pairwise Comparisons

Mazurek

Strzałka²,

Kuras³

2021

IEEE Access

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The aim of this paper is to compare selected iterative algorithms for inconsistency reduction in pairwise comparisons by Monte Carlo simulations. We perform simulations for pairwise comparison matrices of the order n = 4 and n = 8 with the initial inconsistency 0.10 < CR < 0.80 and entries drawn from Saaty's fundamental scale. Subsequently, we evaluate the algorithms' performance with respect to four measures that express the degree of original preference preservation. Our results indicate that no algorithm outperforms all other algorithms with respect to every measure of preference preservation. The Xu and Wei's algorithm is the best with regard to the preservation of an original priority vector and the ranking of objects, the Step-by-Step algorithm best preserves the original preferences expressed in the form of a pairwise comparison matrix, and the algorithm of Szybowski keeps the most matrix entries unchanged during inconsistency reduction.

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Section: Preliminariesmentioning

confidence: 99%

A Numerical Comparison of Iterative Algorithms for Inconsistency Reduction in Pairwise Comparisons

Mazurek

Strzałka²,

Kuras³

2021

IEEE Access

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“…By introducing a more general notion of metric, Cavallo and D´Apuzzo (2009) provided a consistency index that is easy to compute in the additive and multiplicative cases [10]. Mazurek and Ramík (2019) showed that pair wise comparisons matrices is not appropriate [11], hence a new categorization of inconsistent matrices is proposed with respect to a satisfaction of selected logical properties. Hoang and Nguyen (2020) used Fuzzy analytic hierarchy process in the area of rural labor quality evaluation [12].…”

Section: Present State Of Problem Solvingmentioning

confidence: 99%

“…Substitution to the initial formula means the multiplication of individual criteria values according to the calculation: (9) and at the same time multiplication according to the formula: (10) Wang (2008) determined corrected formula as follows. (11) The last used formula is as follows:…”

Section: Fuzzy Analytic Hierarchy Processmentioning

confidence: 99%

Use of Multivariable Decision Methods in Decision of Retail Organizations

Manová¹,

Kopčáková²,

Štofová³

et al. 2021

TEM Journal

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The contribution is orientated to the extended well-known methods of multivariable decisions with a closer specification of Saaty and TOPSIS method. The goal of the contribution is to evaluate the performance of individual operations in the chosen company from eastern Slovakia. According to the results there is obvious several operations in smaller towns, and better results are achieved in comparing with bigger towns, since the bigger towns have higher density of population. Obtained facts can be useful during managerial decisions at the increasing of demands on several bigger operations, with a goal to intensify the performance of the operations in bigger towns.

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“…Therefore, many inconsistency indices have been proposed in the literature and their properties extensively studied, see e.g. [2], [9], [10], [11], [14], [23], [25], [28], [29], [30], or [32].…”

Section: Preliminariesmentioning

confidence: 99%

A New Step-by-Step (SBS) Algorithm for Inconsistency Reduction in Pairwise Comparisons

Mazurek

Strzałka

2020

IEEE Access

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Pairwise comparisons constitute a popular and important tool for multiple-criteria decision making. Consistency is one particular aspect of pairwise comparisons that has been studied thoroughly in recent decades since human judgements are seldom fully consistent. The aim of this paper is to propose a new simple and intuitive iterative Step-by-Step (SBS) algorithm for inconsistency reduction of a (multiplicative) pairwise comparison matrix based on step-by-step changes of the most inconsistent matrix element, where the inconsistency is measured by a modified Koczkodaj's inconsistency index. A comparison of the proposed SBS algorithm with other algorithms for inconsistency reduction is provided as well.

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Some new properties of inconsistent pairwise comparisons matrices

Cited by 25 publications

References 14 publications

A Numerical Comparison of Iterative Algorithms for Inconsistency Reduction in Pairwise Comparisons

A Numerical Comparison of Iterative Algorithms for Inconsistency Reduction in Pairwise Comparisons

Use of Multivariable Decision Methods in Decision of Retail Organizations

A New Step-by-Step (SBS) Algorithm for Inconsistency Reduction in Pairwise Comparisons

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