Analyzing Saaty’s consistency test in pairwise comparison method: a perspective based on linguistic and numerical scale
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The consistency test is a vital basis of the pairwise comparison method, which is performed to ensure that the decision maker is being logical in his/her pairwise comparisons. In the analytic hierarchy process, the pairwise comparison method with a fixed numerical scale has been employed. In this study, we provide a systematic review analysis regarding the inconsistency causes in the pairwise comparison method with a fixed numerical scale, and propose the paradoxes on Saaty’s consistency test in this pairwise comparison method. Meanwhile, based on the use of the consistency-driven linguistic methodology, we propose a novel approach from a perspective of the linguistic and numerical scale to deal with the inconsistency in the pairwise comparison method.
KeywordsMultiple attribute decision making Pairwise comparison matrix Consistency Numerical scale The 2-tuple linguistic representation model Consistency-driven linguistic methodology
This work was supported by the grants (Nos. 71571124, 71171160, 71471065) from NSF of China, the grant (No. skqy201606) from Sichuan University, the grant (No. 2015GD05) from South China University of Technology, the grant (No. GDUPTLAB201602) from the Open Fund of Guangdong Provincial Key Laboratory of Petrochemical Equipment Fault Diagnosis and the grant (No. 2015B090903084) from Guangdong Provincial Science and Technology Cooperation Project.
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Conflict of interest
The authors declare that there is no conflict of interest regarding the publication of this paper.
Human and animal studies
This paper does not contain any studies with human participants or animals performed by any of the authors.
- Cabrerizo FJ, Al-Hmouz R, Morfeq A, Balamash AS, Martínez MA, Herrera-Viedma E (2015a) Soft consensus measures in group decision making using unbalanced fuzzy linguistic information. Soft Comput. doi: 10.1007/s00500-015-1989-6
- Cabrerizo FJ, Chiclana F, Al-Hmouz R, Morfeq A, Balamash AS, Herrera-Viedma E (2015b) Fuzzy decision making and consensus: challenges. J Intell Fuzzy Syst 29:1109–1118Google Scholar
- Golden BL, Wang Q (1990) An alternative measure of consistency. In: Golden BL, Wasil EA, Harker PT (eds) Analytic hierarchy process: applications and studies. Springer, New York, pp 68–81Google Scholar
- Ma D, Zheng X (1991) 9/9-9/1 Scale method of AHP. In: Proceedings of the second international symposium on the AHP. University of Pittsburgh, Pittsburgh, PA, pp 197–202Google Scholar
- Xu WJ, Dong YC, Xiao WL (2008) Is it reasonable for Saatys Consistency Test in the pairwise comparison method? In: 2008 ISECS international colloquium on computing, communication, control, and management, pp 294–298Google Scholar