In order to ascertain and solve a particular Multiple Criteria Decision Making (MCDM) problem, frequently a diverse group of experts must share their knowledge and expertise, and thus uncertainty arises from several sources. In those cases, the Multiplicative Preference Relation (MPR) approach can be a useful technique. An MPR is composed of judgements between any two criteria components which are declared within a crisp rank and to express decision maker(s) (DM) preferences. Consistency of an MPR is obtained when each expert has her/his information and, consequently, her/his judgments free of contradictions. Since inconsistencies may lead to incoherent results, individual Consistency should be sought after in order to make rational choices. In this paper, based on the Hadamard’s dissimilarity operator, a methodology to derive intervals for MPRs satisfying a consistency index is introduced. Our method is proposed through a combination of a numerical and a nonlinear optimization algorithms. As soon as the synthesis of an interval MPR is achieved, the DM can use these acceptably consistent intervals to express flexibility in the manner of her/his preferences, while accomplishing some a priori decision targets, rules and advice given by her/his current framework. Thus, the proposed methodology provides reliable and acceptably consistent Interval MPR, which can be quantified in terms of Row Geometric Mean Method (RGMM) or the Eigenvalue Method (EM). Finally, some examples are solved through the proposed method in order to illustrate our results and compare them with other methodologies.
Decision-making support systems Multiple criteria decision-making Analytic hierarchy process Consistency Multiplicative preference relations Uncertain decision-making
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Campanella, G., Ribeiro, R.A.: A framework for dynamic multiple-criteria decision making. Decis. Support Syst. 52, 52–60 (2011)CrossRefGoogle Scholar
Chiclana, F., Mata, F., Martínez, L., Herrera-Viedma, E., Alonso, S.: Integration of a consistency control module within a consensus decision making model. Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 16(01), 35–53 (2008)CrossRefGoogle Scholar
Dong, Y., Zhang, G., Hong, W.C., Xu, Y.: Consensus models for AHP group decision making under row geometric mean prioritization method. Decis. Support Syst. 49(3), 281–289 (2010)CrossRefGoogle Scholar
Saaty, T.: A ratio scale metric and the compatibility of ratio scales: the possibility of arrow’s impossibility theorem. Appl. Math. Lett. 7(6), 45–49 (1994)MathSciNetCrossRefGoogle Scholar
Srdjevic, B.: Linking analytic hierarchy process and social choice methods to support group decision-making in water management. Decis. Support Syst. 42, 2261–2273 (2007)CrossRefGoogle Scholar
Urena, R., Chiclana, F., Morente-Molinera, J.A., Herrera-Viedma, E.: Managing incomplete preference relations in decision making: a review and future trends. Inf. Sci. 302, 14–32 (2015)MathSciNetCrossRefGoogle Scholar
Wang, L.: Compatibility and group decision making. Syst. Eng. Theory Pract. 20, 92–96 (2002)Google Scholar
Wu, Z., Xu, J.: A consistency and consensus based decision support model for group decision making with multiplicative preference relations. Decis. Support Syst. 52(3), 757–767 (2012)CrossRefGoogle Scholar
Yu, L., Lai, K.: A distance-based group decision-making methodology for multiperson multi-criteria emergency decision support. Decis. Support Syst. 51, 307–315 (2011)CrossRefGoogle Scholar