The limit of inconsistency reduction in pairwise comparisons

Koczkodaj, Waldemar W.; Szybowski, Jacek

doi:10.1515/amcs-2016-0050

Cited by 23 publications

(12 citation statements)

References 15 publications

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“…Some mathematical evidence, to support GM as the method of choice, was also provided in [16]. [17] shows that orthogonal projections have a limit which is GM (to a constant). [18] demonstrates that the inconsistency reduction algorithm based on the orthogonal projections converges very quickly for practical applications.…”

Section: Approximation By Projectionsmentioning

confidence: 99%

On Orthogonal Projections on the Space of Consistent Pairwise Comparisons Matrices

Koczkodaj

Smarzewski

Szybowski

2020

Self Cite

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In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation of a priority vector induced by a pairwise comparison matrix for a given inner product has been introduced.The mathematical elegance of orthogonalization and its universal use in most applied sciences has been the motivating factor for this study. However, the finding of this study that approximations depend on the inner product assumed, is of considerable importance.

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Section: Approximation By Projectionsmentioning

confidence: 99%

On Orthogonal Projections on the Space of Consistent Pairwise Comparisons Matrices

Koczkodaj

Smarzewski

Szybowski

2020

Self Cite

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“…Koczkodaj's consistency index [36,42,46,47,[49][50][51][52][53][54]] not only measures the inconsistency, but it also shows where it is larger, thus guiding the DM to reassess and correct the inconsistency. Additionally, Bozóki and Rapcsák [46] investigated some properties of the PCs matrix inconsistencies of Saaty and Koczkodaj.…”

Section: Issues With Pairwisementioning

confidence: 99%

Exploring Multicriteria Elicitation Model Based on Pairwise Comparisons: Building an Interactive Preference Adjustment Algorithm

Vasconcelos

Mota

2019

Mathematical Problems in Engineering

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Pairwise comparisons have been applied to several real decision making problems. As a result, this method has been recognized as an effective decision making tool by practitioners, experts, and researchers. Although methods based on pairwise comparisons are widespread, decision making problems with many alternatives and criteria may be challenging. This paper presents the results of an experiment used to verify the influence of a high number of preferences comparisons in the inconsistency of the comparisons matrix and identifies the influence of consistencies and inconsistencies in the assessment of the decision-making process. The findings indicate that it is difficult to predict the influence of inconsistencies and that the priority vector may or may not be influenced by low levels of inconsistencies, with a consistency ratio of less than 0.1. Finally, this work presents an interactive preference adjustment algorithm with the aim of reducing the number of pairwise comparisons while capturing effective information from the decision maker to approximate the results of the problem to their preferences. The presented approach ensures the consistency of a comparisons matrix and significantly reduces the time that decision makers need to devote to the pairwise comparisons process. An example application of the interactive preference adjustment algorithm is included.

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“…As a result, quality of perception of the comparisons will be reduced. To solve this problem, different ways to improve the consistency of judgements have been discussed [71,72]. Another solution is to use incomplete pairwise comparisons [73,74].…”

Section: Limitationsmentioning

confidence: 99%

Artificial intelligence in the synthesis of creative solutions

Андрейчиков¹,

Andreychikov

Андрейчикова³

et al. 2019

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Invention problem solving is connected to essential expenses of labour and time, which is spent on the procedures of search and ordering of necessary knowledge, on generation of probable vari-ants of projected systems, on the analysis of offered ideas and de-cisions and understanding perspectiveness of them. The present article outlines the results of the developments in the field of cre-ating computing technology of the synthesis of new engineering on the level of invention. The most attention is paid to problem of computer aided designing on initial stages, where synthesis of new on principal technical systems is carried out. Computer-aided con-struction of new technical system is based on using of data- and knowledge bases of physical effects and of technical decisions as well as different heuristic systematization procedures. The synthe-sis of principles of function of the technical new systems is carried out with using experts knowledge and requires the application of the artificial intelligence methods and the methods of the deci-sions making theory for invention's tasks. Considered approach has been used for synthesis of new technical systems of different functional purposes and had shown high efficiency in computer-aided construction.

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The limit of inconsistency reduction in pairwise comparisons

Cited by 23 publications

References 15 publications

On Orthogonal Projections on the Space of Consistent Pairwise Comparisons Matrices

On Orthogonal Projections on the Space of Consistent Pairwise Comparisons Matrices

Exploring Multicriteria Elicitation Model Based on Pairwise Comparisons: Building an Interactive Preference Adjustment Algorithm

Artificial intelligence in the synthesis of creative solutions

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