Published Apr 20, 2016
Vitaliy V Tsyganok Sergii V Kadenko Oleh V Andriichuk


In this paper we suggest an original approach to conducting individual pair comparisons during individual and group multi-criteria decision-making (including AHP/ANP-based decisions). With this approach every expert is given an opportunity to use the scale, in the degree of detail (number of points/grades) that most adequately reflects his/her competence in the issue under consideration for every single pair comparison. Before aggregation all separate expert estimates (judgments) are brought to a unified scale, and scales in which these judgments were built are assigned respective weights. A respective instrument for pair comparison conduction has been developed, and an experiment has been organized. The experiment statistically proves that as a result of suggested technology usage, there is an increase in the degree of correspondence between estimates, input by an expert, and his (her) own notions on examination objects.

How to Cite

Tsyganok, V. V., Kadenko, S. V., & Andriichuk, O. V. (2016). USAGE OF SCALES WITH DIFFERENT NUMBER OF GRADES FOR PAIR COMPARISONS IN DECISION SUPPORT SYSTEMS. International Journal of the Analytic Hierarchy Process, 8(1).


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Group decision making, decision support system, expert judgments, pairwise comparisons, different scales

De Felice, F., & Petrillo, A. (2013a). Multicriteria approach for process modelling in strategic environmental management planning. International Journal of Simulation and Process Modelling, 8(1), 6–16. doi:

De Felice, F., & Petrillo, A. (2013b). Decision-making analysis to improve public participation in strategic energy production management. Studies in Fuzziness and Soft Computing 305, 129–142. doi: 10.1007/978-3-642-35635-3_11

Dodd, F.J., Donegan, H.A., & McMaster, T.B.M. (1995). Scale horizons in analytic hierarchies. Journal of Multi-criteria Decision Analysis, 4, 177–188. doi: 10.1002/mcda.4020040304

Yucheng Dong, Yinfeng Xu, Hongyi Li, & Min Dai (2008). A comparative study of the numerical scales and the prioritization methods in AHP. European Journal of Operational Research, 186, 229–242. doi:10.1016/j.ejor.2007.01.044

Elliott, M.A. (2010). Selecting numerical scales for pairwise comparisons. Reliability Engineering and System Safety, 95, 750–763. doi:10.1016/j.ress.2010.02.013

Hartley, R.V.L. (1928). Transmission of information. Bell System Technical Journal, 7, 535–63. doi: 10.1002/j.1538-7305.1928.tb01236.x

Ji, P., & Jiang, R. (2003). Scale transitivity in the AHP. Journal of the Operational Research Society, 54(8), 896–905. doi:10.1057/palgrave.jors.2601557

Kalika, V.I., & Rossinsky, G. (2003). Methodology of multi-criteria decision making accounting for uncertainty and some applications. International Journal of Management and Decision Making, 4(2/3), 240 – 271. doi:

Kannan, G., Noorul Haq, A., & Sasikumar, P. (2008) An application of the Analytical Hierarchy Process and Fuzzy Analytical Hierarchy Process in the selection of collecting centre location for the reverse logistics. Multicriteria Decision-Making supply chain model. International Journal of Management and Decision Making, 9(4), 350 – 365. doi:

Lootsma F.A. (1989). Conflict resolution via pairwise comparisons of concessions. European Journal of Operational Research, 40, 109–116. doi:10.1016/0377-2217(89)90278-6

Lootsma F.A. (1991). Scale sensitivity and rank preservation in a multiplicative variant of the AHP and SMART. Report 91–67. Faculty TWI. Delft University of Technology. Delft. The Netherlands.

Ma, D., & Zheng, X. (1991). Scale method of AHP. Proceedings of the Second International Symposium on the AHP, 1, 197–202.

Miller, G.A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. The Psychological Review, 63(2), 81–97.

Noorul Haq, A., & Kannan, G. (2007). A hybrid normalised multi criteria decision making for the vendor selection in a supply chain model. International Journal of Management and Decision Making, 8 (5/6), 601–622. doi:

Saaty, T.L. (2006). Fundamentals of decision making and priority theory with the analytic hierarchy process. Pittsburgh, PA: RWS Publications.

Saaty T.L. (2008). Relative measurement and its generalization in decision making. Why pairwise comparisons are central in mathematics for the measurement of intangible factors. The Analytic Hierarchy/Network Process. Statistics and Operations Research, 102(2), 251–318. doi:10.1007/BF03191825

Salo, A.A., & Hamalainen, R.P. (1997). On the measurement of preferences in the analytic hierarchy process. Journal of Multi-criteria Decision Analysis, 6, 309–319. doi: 10.1002/(SICI)1099-1360(199711)6:6<309::AID-MCDA163>3.0.CO;2-2

Stevens, S.S. (1957). On the psychophysical law. Psychology Review, 64, 153–181. doi:

Tsyganok, V.V. (2010). Investigation of the aggregation effectiveness of expert estimates obtained by the pairwise comparison method. Mathematical and Computer Modelling, 52(3-4), 538–544. doi:10.1016/j.mcm.2010.03.052

Vaidogas, E.R., & Zavadskas, E.K. (2007). Introducing reliability measures into multi-criteria decision-making. International Journal of Management and Decision Making, 8(5/6), 475 – 496. doi:

Wedley, W.C., & Eng Ung Choo (2010). A taxonomy of ratio scales. OR-52 Keynotes and Extended Abstracts, Operational Research Society Ltd., Royal Holloway University of London, UK 7-9/09/2010, 199–203.

Zandi, F. & Tavana, M. (2010). A multi-attribute group decision support system for information technology project selection. International Journal of Business Information Systems, 6(2), 179 – 199. doi:

Zgurovsky, M.Z., Totsenko, V.V., & Tsyganok, V.V. (2004). Group incomplete paired comparisons with account of expert competence. Mathematical and Computer Modelling, 39(4), 349–361. doi:10.1016/S0895-7177(04)90511-0