Previous |  Up |  Next


Fuzzy; group decision-making; multicriteria evaluation; fuzzy weighted average; consensus reaching; fuzzy quantifiers
The paper introduces a new method of reaching a consensus in multiple criteria group decision-making under fuzziness. This model is based on the general definition of the ‘soft’ consensus introduced by Kacprzyk and Fedrizzi in 1986. The fuzzy evaluations of alternatives express degrees of fulfillment of the given goals by the respective alternatives for each expert. The selection of the best alternative is based on the fuzzy consensus by experts. For this purpose a set of alternatives which are good enough with respect to the most of relevant experts is identified. From this set the alternative with the highest center of gravity (defuzzified fuzzy evaluation) is selected as the most promising one.
[1] Alonso, S.: Group Decision Making with Incomplete Fuzzy Preference Relations. Ph.D. Thesis, Universidad de Granada, Granada, 2006.
[2] Arrow, K. J.: Social Choice and Individual Values. 2nd edition, Wiley, New York, 1963.
[3] Bouyssou, D., Dubois, D., Pirlot, M., Prade, H.: Decision-making Process: Concepts and Methods. Wiley, New York, 2009.
[4] Bustince, H.: Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. STUDFUZZ 220, Springer, Berlin, Heidelberg, 2008. Zbl 1130.68004
[5] Cabrerizo, F. J., Pérez, I. J., Herrera-Viedma, E.: Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information. Knowledge-Based Systems 23 (2010), 169–181. DOI 10.1016/j.knosys.2009.11.019
[6] Çağman, N., Wang, X.: A new group decision-making method based on fuzzy set operations. European Journal of Pure and Applied Mathematics 4, 1 (2011), 42–49. Zbl 1231.91063
[7] Calvo, T., Beliakov, G.: Aggregation functions bsed on penalties. Fuzzy Sets and Systems 161 (2010), 1420–1436. DOI 10.1016/j.fss.2009.05.012 | MR 2606423
[8] Eklund, P., Rusinowska, A., De Swart, H.: Consensus reaching in committees. European Journal of Operational Research 178 (2007), 185–193. DOI 10.1016/j.ejor.2005.11.012 | Zbl 1102.90337
[9] Kacprzyk, J., Fedrizzi, M.: ‘Soft’ consensus measures for monitoring real consensus reaching processes under fuzzy preferences. Control and Cybernetics 15 (1986), 309–323. MR 0906878
[10] Kacprzyk, J., Roubens, M.: Non-Conventional Preference Relations in Decision Making. Springer-Verlag, Berlin, Heidelberg, 1988. MR 1133644 | Zbl 0642.00025
[11] Kacprzyk, J., Fedrizzi, M., Nurmi, H.: ‘Soft’ degrees of consensus under fuzzy preferences and fuzzy majorities. In: J., Kacprzyk et al. (eds.): Consensus under Fuzziness, Springer Science & Business Media, New York, 1997, 55–83.
[12] Kacprzyk, J., Nurmi, H., Fedrizzi, M.: Consensus under Fuzziness. Springer Science & Business Media, New York, 1997. Zbl 0882.00024
[13] Klamler, C.: The Dodgson ranking and the Borda count: a binary comparison. Mathematical Social Sciences 48 (2004), 103–108. DOI 10.1016/j.mathsocsci.2003.11.003 | MR 2054547 | Zbl 1091.91020
[14] González-Pachón, J., Romero, C.: Distance-based consensus methods: a goal programming approach. Omega, International Journal of Management Science 27 (1999), 341–347. DOI 10.1016/S0305-0483(98)00052-8
[15] Herrera-Viedma, E.: Consensual Processes. STUDFUZZ 267, Springer-Verlag, Berlin, Heidelberg, 2011.
[16] Herrera, F., Herrera-Viedma, E., Verdegay, J. L.: A rational consensus model in group decision making using linguistic assessments. Fuzzy Sets and Systems 88 (1997), 31–49. DOI 10.1016/S0165-0114(96)00047-4
[17] Herrera, F., Herrera-Viedma, E., Verdegay, J. L.: A model of consensus in group decision making using linguistic assessments. Fuzzy Sets and Systems 78 (1996), 73–87. DOI 10.1016/0165-0114(95)00107-7 | MR 1376216
[18] Holeček, P., Talašová, J., Müller, I.: Fuzzy methods of multiple-criteria evaluation and their software implementation. In: V. K., Mago, N., Bhatia (eds.): Cross-Disciplinary Applications of Artificial Intelligence and Pattern Recognition: Advancing Technologies, IGI Global 2012, 388–411.
[19] Kelly, J. S.: Social Choice Theory. Springer-Verlag, Berlin, Heidelberg, New York, 1988. Zbl 0689.90002
[20] Maskin, E.: The Arrow Impossibility Theorem. Columbia University Press, New York, 2014.
[21] Pavlačka, O., Talašová, J.: Fuzzy vectors of normalized weights and their application in decision making models. Aplimat – Journal of Applied Mathematics 1, 1 (2008), 451–462.
[22] Pavlačka, O., Talašová, J.: Fuzzy vectors as a tool for modeling uncertain multidimensional quantities. Fuzzy Sets and Systems 161 (2010), 1585–1603. DOI 10.1016/j.fss.2009.12.008 | MR 2608263 | Zbl 1186.90144
[23] Pavlačka, O.: Modeling uncertain variables of the weighted average operation by fuzzy vectors. Information Sciences 181 (2011), 4969–4992. DOI 10.1016/j.ins.2011.06.022 | MR 2832874 | Zbl 1241.68117
[24] Slowiński, R.: Fuzzy Sets in Decision Analysis, Operations Research and Statistics. Springer Science & Business Media, New York, 1998. MR 1672362 | Zbl 0905.00031
[25] Talašová, J.: Fuzzy metody vícekriteriálního hodnocení a rozhodování. Vydavatelství UP, Olomouc, 2003, (in Czech).
[26] Talašová, J., Pavlačka, O.: Fuzzy probability spaces and their applications in decision making. Austrian Journal of Statistics. 35, 2 & 3 (2006), 347–356.
[27] Zadeh, L. A.: Fuzzy sets. Information and Control 8, 3 (1965), 338–353. DOI 10.1016/S0019-9958(65)90241-X | MR 0219427 | Zbl 0139.24606
[28] Zadeh, L. A.: The concept of a linguistic variable and its application to approximate reasoning-I. Information Sciences 8, 3 (1975), 199–249. MR 0386369 | Zbl 0397.68071
Partner of
EuDML logo