Abstract
A method of a computer support for an expert who is creating a matrix of pairwise preferences in a decision making problem is described. The final preference matrix should be antisymmetric and consistent. While it is easy to control the antisymmetricity of the entries, the consistency of the inserted values, on the other hand, is far from obvious. The suggested computer support is based on the idea that the consistent hull of the previously inserted entries is maintained in the computer, and in every step the human expert gets the information whether the intended preference value can be chosen independently of the previous inputs. If the opposite case, then computer recommends the unique consistent value. Still, the expert can decide differently according to his/her own opinion. Then the optimal consistent approximation of all previous entries including the last input is computed and maintained for further steps. The computer support uses the optimal approximation algorithm due to the authors. The new method is illustrated by examples.
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References
Aguaron, J., Escobar, M.T., Moreno-Jimenez, J.M.: Consistency stability intervals for a judgement in AHP decision support systems. Eur. J. Oper. Res. 145(2), 382–393 (2003)
Carlsson, C., Fuller, R.: Fuzzy multiple criteria decision making: recent developments. Fuzzy Sets Syst. 78(2), 139–153 (1996)
Dytczak, M., Szklennik, N.: Principles and applications of AHP/ANP-based multiple MCDA methods approach. In: Proceedings of ISAHP (2011)
Gavalec, M., Tomášková, H.: Optimal consistent approximation of a preference matrix in decision making. Int. J. Math. Oper. Res.
Gavalec, M., Ramk, J., Zimmermann, K.: Decision Making and Optimization: Special Matrices and Their Applications in Economics and Management, vol. 677. Springer, Berlin (2014)
Jalao, E.R., Wu, T., Shunk, D.: A stochastic AHP decision making methodology for imprecise preferences. Inf. Sci. 270, 192–203 (2014)
Leung, L., Cao, D.: On consistency and ranking of alternatives in fuzzy AHP. Eur. J. Oper. Res. 124(1), 102–113 (2000)
Mls, K., Gavalec, M.: Multi-criteria models in autonomous decision making systems. In: Proceedings of the 10th International Symposium on the Analytic Hierarchy/Network Process, pp. 1–8 (2009)
Ramik, J., Korviny, P.: Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean. Fuzzy Sets Syst. 161(11), 1604–1613 (2010)
Ramik, J., Perzina, R.: A method for solving fuzzy multicriteria decision problems with dependent criteria. Fuzzy Optim. Decis. Making 9(2), 123–141 (2010)
Saaty, T.L.: Decision-making with the AHP: why is the principal eigenvector necessary. Eur. J. Oper. Res. 145(1), 85–91 (2003)
Satty, T.L., et al.: The analytic hierarchy process (1980)
Vargas, L.G.: Reciprocal matrices with random coefficients. Math. Model. 3(1), 69–81 (1982)
Zahedi, F.: The analytic hierarchy process: a survey of the method and its applications. Interfaces 16(4), 96–108 (1986)
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The support of SPEV UHK FIM is gratefully acknowledged.
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Gavalec, M., Tomášková, H., Cimler, R. (2016). Computer Support in Building-up a Consistent Preference Matrix. In: Sulaiman, H., Othman, M., Othman, M., Rahim, Y., Pee, N. (eds) Advanced Computer and Communication Engineering Technology. Lecture Notes in Electrical Engineering, vol 362. Springer, Cham. https://doi.org/10.1007/978-3-319-24584-3_80
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DOI: https://doi.org/10.1007/978-3-319-24584-3_80
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