Abstract
Linguistic pairwise comparison matrices for decision-making need to be (strongly) order-consistent, which means the judgments should be (strongly) transitive. We introduce the equivalent conditions of (strong) transitivity by using route matrices and digraphs and develop an adjustment procedure to help decision makers correcting the inconsistency. The conclusion can extend to other ordinal-scaled or numerical comparison matrices as well.
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Acknowledgments
We sincerely thank the editors and four anonymous referees. Their careful and detailed comments helped us improve the paper considerably. This work was supported by the National Natural Science Foundation of China (Nos. 71401185, 71431008); MOE (Ministry of Education in China) Project of Humanities and Social Sciences (No. 13YJC630200); China Postdoctoral Science Foundation (Nos. 2015T80869, 2014M552135); and Hunan Provincial Natural Science Foundation of China (No. 14JJ4050).
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Yang, WE., Ma, CQ., Han, ZQ. et al. Checking and adjusting order-consistency of linguistic pairwise comparison matrices for getting transitive preference relations. OR Spectrum 38, 769–787 (2016). https://doi.org/10.1007/s00291-015-0417-8
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DOI: https://doi.org/10.1007/s00291-015-0417-8