Abstract
In this paper we compare, by means of numerical simulations, seven different methods for reconstructing incomplete fuzzy preference relations. We consider the case of highly inconsistent preference relations as well as the case of preference relations close to consistency. We compare the numerical results on the basis of the consistency of the reconstructed preference relations.
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References
Barzilai, J.: Consistency measures for pairwise comparison matrices. J. Multi–Crit. Decis. Anal. 7, 123–132 (1998)
Brunelli, M., Fedrizzi, M.: A note on the paper Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation, submitted to International Journal of Approximate Reasoning (2007)
Chen, Q., Triantaphyllou, E.: Estimating Data for Multi–Criteria Decision Making Problems: Optimization Techniques. In: Pardalos, P.M., Floudas, C. (eds.) Encyclopedia of Optimization, vol. 2, Kluwer Academic Publishers, Boston, MA (2001)
Chiclana, F., Herrera, F., Herrera–Viedma, E.: Integrating multiplicative preference relations in a multipurpose decision–making model based on fuzzy preference relations. Fuzzy Sets and Systems 122, 277–291 (2001)
Chu, A.T.W., Kalaba, R.E., Springarn, K.: A comparison of two methods for determining the weights of belonging to fuzzy sets. J. Optim. Th. Appl. 27, 321–538 (1979)
Fedrizzi, M.: On a consensus measure in a group MCDM problem. In: Kacprzyk, J., Fedrizzi, M. (eds.) Multiperson Decision Making Models using Fuzzy Sets and Possibility Theory (Theory and Decision Library, series B: Mathematical and Statistical Methods, Vol. 18), Kluwer Academic Publishers, Dordrecht, The Netherlands (1990)
Fedrizzi, M., Giove, S.: Incomplete pairwise comparison and consistency optimization. European Journal of Operational Research (2006) doi: 10.1016/ j.ejor.2006.09.065
Harker, P.T.: Alternative modes of questioning in the analytic hierarcy process. Mathl Modelling 9(3-5), 353–360 (1987)
Harker, P.T.: Incomplete pairwise comparisons in the analytic hierarcy process. Mathl Modelling 9(11), 837–848 (1987)
Herrera–Viedma, E., Herrera, F., Chiclana, F., Luque, M.: Some Issues on Consistency of Fuzzy Preference Relations. European Journal of Operational Research 154, 98–109 (2004)
Herrera–Viedma, E., Chiclana, F., Herrera, F., Alonso, S.: Group decision-making model with incomplete fuzzy preference relations based on additive consistency. IEEE Trans. Syst. Man. Cybern. B. Cybern. 37(1), 176–189 (2007)
Kacprzyk, J., Roubens, M.: Non–Conventional Preference Relations in Decision–Making. Springer, Berlin (1988)
Kwiesielewicz, M.: The logaritmic least squares and the generalized pseudoinverse in estimating ratios. European Journal of Operational Research 93, 611–619 (1996)
Kwiesielewicz, M., van Uden, E.: Ranking Decision Variants by Subjective Paired Comparisons in Cases with Incomplete Data. In: Kumar, V. (ed.) ICCSA 2003. LNCS, vol. 2667, Springer, Heidelberg (2003)
Nishizawa, K.: Estimation of unknown comparisons in incomplete AHP and it’s compensation. Report of the Research Institute of Industrial Technology, Nihon University (77) (2004)
Orlovsky, S.A.: Decision–making with a fuzzy preference relation. Fuzzy Sets and Systems 1, 155–167 (1978)
Peláez, J.I., Lamata, M.T.: A new measure of consistency for positive reciprocal matrices. Computers and Mathematics with Applications 46, 1839–1845 (2003)
Saaty, T.L.: The Analytical Hierarchy Process. McGraw-Hill, New York (1980)
Saaty, T.L., Vargas, L.G.: Models, methods, concepts & applications of the analythical hierarchy process. Kluwer Academic, Boston (2001)
Shiraishi, S., Obata, T., Daigo, M.: Properties of a positive reciprocal matrix and their application to AHP. J. Oper. Res. Soc. Japan 41, 404–414 (1998)
Takeda, E., Yu, P.L.: Assessing priority weights from subsets of pairwise comparisons in multiple criteria optimization problems. European Journal of Operational Research 86, 315–331 (1995)
Tanino, T.: Fuzzy preference orderings in group decision making. Fuzzy Sets and Systems 12, 117–131 (1984)
van Uden, E.: Estimating missing data in pairwise comparison matrices. In: Bubnicki, Z., Hryniewicz, O., Kulikowski, R. (eds.) Operational and Systems Research in the Face to Challenge the XXI Century, Methods and Techniques in Information Analysis and Decision Making, Academic Printing House, Warsaw (2002)
Xu, Z.S.: Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation. International Journal of Approximate Reasoning 36, 261–270 (2004)
Xu, Z.S.: A procedure for decision making based on incomplete fuzzy preference relation. Fuzzy Optimization and Decision Making 4, 175–189 (2005)
Xu, Z.S.: A least deviation method to obtain a priority vector of a fuzzy preference relation. European Journal of Operational Research 164, 206–216 (2005)
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Brunelli, M., Fedrizzi, M., Giove, S. (2007). Reconstruction Methods for Incomplete Fuzzy Preference Relations: A Numerical Comparison. In: Masulli, F., Mitra, S., Pasi, G. (eds) Applications of Fuzzy Sets Theory. WILF 2007. Lecture Notes in Computer Science(), vol 4578. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73400-0_11
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DOI: https://doi.org/10.1007/978-3-540-73400-0_11
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