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Analysis of pairwise comparison matrices: an empirical research

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  • Sándor Bozóki
  • Linda Dezső
  • Attila Poesz
  • József Temesi

Abstract

Pairwise comparison (PC) matrices are used in multi-attribute decision problems (MADM) in order to express the preferences of the decision maker. Our research focused on testing various characteristics of PC matrices. In a controlled experiment with university students (N=227) we have obtained 454 PC matrices. The cases have been divided into 18 subgroups according to the key factors to be analyzed. Our team conducted experiments with matrices of different size given from different types of MADM problems. Additionally, the matrix elements have been obtained by different questioning procedures differing in the order of the questions. Results are organized to answer five research questions. Three of them are directly connected to the inconsistency of a PC matrix. Various types of inconsistency indices have been applied. We have found that the type of the problem and the size of the matrix had impact on the inconsistency of the PC matrix. However, we have not found any impact of the questioning order. Incomplete PC matrices played an important role in our research. The decision makers behavioral consistency was as well analyzed in case of incomplete matrices using indicators measuring the deviation from the final order of alternatives and from the final score vector. Copyright Springer Science+Business Media New York 2013

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  • Sándor Bozóki & Linda Dezső & Attila Poesz & József Temesi, 2013. "Analysis of pairwise comparison matrices: an empirical research," Annals of Operations Research, Springer, vol. 211(1), pages 511-528, December.
    • Handle: RePEc:spr:annopr:v:211:y:2013:i:1:p:511-528:10.1007/s10479-013-1328-1
    DOI: 10.1007/s10479-013-1328-1
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    9. Vladimír Bureš & Jiří Cabal & Pavel Čech & Karel Mls & Daniela Ponce, 2020. "The Influence of Criteria Selection Method on Consistency of Pairwise Comparison," Mathematics, MDPI, vol. 8(12), pages 1-13, December.
    10. Tarján, Tamás & Veres, Zoltán, 2018. "Szekvenciális fogyasztói termékválasztás döntési kontinuuma [The decision-making continuum of sequential consumer-product choices]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(5), pages 525-550.
    11. Matteo Brunelli, 2017. "Studying a set of properties of inconsistency indices for pairwise comparisons," Annals of Operations Research, Springer, vol. 248(1), pages 143-161, January.
    12. Zsombor Szádoczki & Sándor Bozóki & Patrik Juhász & Sergii V. Kadenko & Vitaliy Tsyganok, 2023. "Incomplete pairwise comparison matrices based on graphs with average degree approximately 3," Annals of Operations Research, Springer, vol. 326(2), pages 783-807, July.
    13. Brunelli, Matteo, 2019. "A study on the anonymity of pairwise comparisons in group decision making," European Journal of Operational Research, Elsevier, vol. 279(2), pages 502-510.

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