Abstract
In Group Decision Making (GDM) the automatic consensus models are guided by different consensus measures which usually are obtained by aggregating similarities observed among experts’ opinions. Most GDM problems based on linguistic approaches use symmetrically and uniformly distributed linguistic term sets to express experts’ opinions.However, there exist problemswhose assessments need to be represented by means of unbalanced linguistic term sets, i.e., using term sets which are not uniformly and symmetrically distributed. The aim of this paper is to present different Linguistic OWA Operators to compute the consensus measures in consensusmodels for GDMproblems with unbalanced fuzzy linguistic information.
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References
Bezdek, J., Spillman, B., Spillman, R.: Fuzzy measures of preferences and consensus in group decision making. In: Proc. 1977 IEEE Conf. on Decision and Control, pp. 1303–1309 (1977)
Bezdek, J., Spillman, B., Spillman, R.: A fuzzy relation space for group decision theory. Fuzzy Sets and Systems 1, 255–268 (1978)
Bilgiç, T.: Interval–valued preference structures. European Journal of Operational Research 105(1), 162–183 (1998)
Cabrerizo, F.J., Alonso, S., Herrera-Viedma, E.: A consensus model for group decision making problems with unbalanced fuzzy linguistic information. International Journal of Information Technology & Decision Making 8(1), 109–131 (2009)
Chen, S.J., Hwang, C.L.: Fuzzy multiple attributive decision making: Theory and its applications. Springer, Berlín (1992)
Chiclana, F., Herrera, F., Herrera-Viedma, E.: Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets and Systems 97(1), 33–48 (1998)
Chiclana, F., Herrera, F., Herrera-Viedma, E.: A note on the internal consistency of various preference representations. Fuzzy Sets and Systems 131(1), 75–78 (2002)
Chiclana, F., Herrera, F., Herrera-Viedma, E., Martínez, L.: A note on the reciprocity in the aggregation of fuzzy preference relations using owa operators. Fuzzy Sets and Systems 137(1), 71–83 (2004)
Chiclana, F., Herrera-Viedma, E., Herrera, F., Alonso, S.: Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations. European Journal of Operational Research 182(1), 383–399 (2007)
Chiclana, F., Herrera-Viedma, E., Alonso, S., Herrera, F.: Cardinal Consistency of Reciprocal Preference Relations: A Characterization of Multiplicative Transitivity. IEEE Transactions on Fuzzy Systems 17(1), 14–23 (2009)
Chiclana, F., Mata, F., Martínez, L., Herrera-Viedma, E., Alonso, S.: Integration of a consistency control module within a consensus model. International Journal of Uncertainty, Fuzziness and Knowledge Based Systems 16(1), 35–53 (2008)
Cialdini, R.B.: Influence: science and practice, 4th edn. Allyn and Bacon, Boston (2001)
Fedrizzi, M., Fedrizzi, M., Marques Pereira, R.A.: On the issue of consistency in dynamical consensual aggregation. In: Bouchon-Meunier, B., Gutierrez-Ros, J., Magdalena, L., Yager, R.R. (eds.) Technologies for Constructing Intelligent Systems 1: Tasks. Studies in Fuzziness and Soft Computing, pp. 129–138. Physica-Verlag, Berlin (2002)
Fodor, J., Roubens, M.: Fuzzy preference modelling and multicriteria decision support. Kluwer, Dordrecht (1994)
Herrera, F., Herrera–Viedma, E.: Linguistic decision analysis: steps for solving decisions problems under linguistic information. Fuzzy Sets and Systems 115, 67–82 (2000)
Herrera, F., Herrera-Viedma, E., Chiclana, F.: Multiperson decision making based on multiplicative preference relations. European Journal of Operational Research 129, 372–385 (2001)
Herrera, F., Herrera-Viedma, E., Martínez, L.: A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Transactions on Fuzzy Systems 16(2), 354–370 (2008)
Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: A model of consensus in group decision making under linguistic assessments. Fuzzy Sets and Systems 78(1), 73–87 (1996)
Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: A linguistic decision process in group decision making. Group Decision and Negotiation 5, 165–176 (1996)
Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: Direct approach processes in group decision making using linguistic owa operators. Fuzzy Sets and Systems 79, 175–190 (1996)
Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: A rational consensus model in group decision making using linguistic assessments. Fuzzy Sets and Systems 88(1), 31–49 (1997)
Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: Linguistic measures based on fuzzy coincidence for reaching consensus in group decision making. Int. J. of Approximate Reasoning 16(3-4), 309–334 (1997)
Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: Choice processes for non-homogeneous group decision making in linguistic setting. Fuzzy Sets and Systems 94, 287–308 (1998)
Herrera, F., Martínez, L.: A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems 8(6), 746–752 (2000)
Herrera, F., Martínez, L.: A model based on linguistic 2-tuples for dealing with multigranularity hierarchical linguistic contexts in multiexpert decision-making. IEEE Transactions on Systems, Man and Cybernetics. Part B: Cybernetics 31(2), 227–234 (2001)
Herrera-Viedma, E., Alonso, S., Herrera, F., Chiclana, F.: A consensus model for group decision making with incomplete fuzzy preference relations. IEEE Transactions on Fuzzy Systems 15(5), 863–877 (2007)
Herrera-Viedma, E., Chiclana, F., Herrera, F., Alonso, S.: A group decision-making model with incomplete fuzzy preference relations based on additive consistency. IEEE Transactions on Systems, Man and Cybernetics, Part B, Cybernetics 37(1), 176–189 (2007)
Herrera-Viedma, E., Herrera, F., Chiclana, F.: A consensus model for multiperson decision making with different preference structures. IEEE Transactions on Systems, Man and Cybernetics-Part A: Systems and Humans 32(3), 394–402 (2002)
Herrera-Viedma, E., Herrera, F., Chiclana, F., Luque, M.: Some issues on consistency of fuzzy preference relations. European Journal of Operational Research 154(1), 98–109 (2004)
Herrera-Viedma, E., López-Herrera, A.G.: A model of information retrieval system with unbalanced fuzzy linguistic information. International Journal of Intelligent Systems 22(11), 1197–1214 (2007)
Herrera-Viedma, E., Martínez, L., Mata, F., Chiclana, F.: A consensus support system model for group decision-making problems with multi-granular linguistic preference relations. IEEE Transaction on Fuzzy Systems 13(5), 644–658 (2005)
Kacprzyk, J.: Group decision making with a fuzzy linguistic majority. Fuzzy Sets and Systems 18, 105–118 (1986)
Kacprzyk, J.: On some fuzzy cores and soft consensus measures in group decision making. In: Bezdek, J. (ed.) The Analysis of Fuzzy Information, pp. 119–130. CRC Press, Boca Raton (1987)
Kacprzyk, J., Fedrizzi, M.: Soft consensus measure for monitoring real consensus reaching processes under fuzzy preferences. Control Cybernet 15, 309–323 (1986)
Kacprzyk, J., Fedrizzi, M.: A soft measure of consensus in the setting of partial (fuzzy) preferences. European Journal of Operational Research 34, 316–323 (1988)
Kacprzyk, J., Fedrizzi, M., Nurmi, H.: Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets and Systems 49(1), 21–31 (1992)
Kacprzyk, J., Nurmi, H., Fedrizzi, M.: Consensus under fuzziness. Kluwer Academic Publishers, Boston (1997)
Levrat, E., Voisin, A., Bombardier, S., Bremont, J.: Subjective evaluation of car seat comfort with fuzzy set techniques. International Journal of Intelligent Systems 12(12), 891–913 (1997)
Mata, F., Martínez, L., Herrera-Viedma, E.: An adaptive consensus support model for group decision making problems in a multi-granular fuzzy linguistic context. IEEE Transaction on Fuzzy Systems 17(2), 279–290 (2009)
Marakas, G.H.: Decision Support Systems in the 21th Century, 2nd edn. Pearson Education, Upper Saddle River (2003)
Roubens, M.: Fuzzy sets and decision analysis. Fuzzy Sets and Systems 90(2), 199–206 (1997)
Saaty, T.L.: The analytic hierarchy process. MacGraw-Hill, New York (1980)
Spillman, B., Bezdek, J., Spillman, R.: Coalition analysis with fuzzy sets. Kybernetes 8, 203–211 (1979)
Spillman, B., Spillman, R., Bezdek, J.: A fuzzy analysis of consensus in small groups. In: Wang, P.P., Chang, S.K. (eds.) Fuzzy Automata and Decision Processes, pp. 331–356. North-Holland, Amsterdam (1980)
Tanino, T.: Fuzzy preference orderings in group decision making. Fuzzy Sets and Systems 12, 117–131 (1984)
Xu, Z.S.: An approach to group decision making based on incomplete linguistic preference relations. International Journal of Information Technology & Decision Making 4(1), 153–160 (2005)
Xu, Z.S.: A method for multiple attribute decision making with incomplete weight information in linguistic setting. Knowledge-Based Systems 20(8), 719–725 (2007)
Yager, R.R.: On Ordered Weighted Averaging Aggregation Operators in Multicriteria Decision Making. IEEE Transactions on Systems, Man, and Cybernetics 18, 183–190 (1988)
Yager, R.R.: Quantifier guided aggregation using OWA operators. International Journal of Intelligent Systems 11(1), 49–73 (1996)
Yager, R.R.: Induced aggregation operators. Fuzzy Sets and Systems 137(1), 59–69 (2003)
Yager, R.R., Filev, D.P.: Operations for granular computing: mixing words and numbers. In: Proceedings of the FUZZ-IEEE World Congress on Computational Intelligence, Anchorage, pp. 123–128 (1998)
Yager, R.R., Filev, D.P.: Induced ordered weighted averaging operators. IEEE Transactions on Systems, Man, and Cybernetics 29(2), 141–150 (1999)
Zadeh, L.A.: The concept of a linguistic variable and its applications to approximate reasoning. Part I. Information Sciencies 8(3), 199–249 (1975)
Zadeh, L.A.: The concept of a linguistic variable and its applications to approximate reasoning. Part II. Information Sciencies 8(4), 301–357 (1975)
Zadeh, L.A.: The concept of a linguistic variable and its applications to approximate reasoning. Part III. Information Sciencies 9(1), 43–80 (1975)
Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Computers and Mathematics with Applications 9(1), 149–184 (1983)
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Herrera-Viedma, E., Cabrerizo, F.J., Pérez, I.J., Cobo, M.J., Alonso, S., Herrera, F. (2011). Applying Linguistic OWA Operators in Consensus Models under Unbalanced Linguistic Information. In: Yager, R.R., Kacprzyk, J., Beliakov, G. (eds) Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice. Studies in Fuzziness and Soft Computing, vol 265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17910-5_9
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DOI: https://doi.org/10.1007/978-3-642-17910-5_9
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