### Impacto

Montero de Juan, Francisco Javier
(2008)
*The impact of fuzziness in social choice paradoxes.*
Soft Computing, 12
(2).
pp. 177-182.
ISSN 1432-7643

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Official URL: http://www.springerlink.com/content/p445288l4n21152h/fulltext.pdf

## Abstract

Since Arrow's main theorem showed the impossibility of a rational procedure in group decision making, many variations in restrictions and objectives have been introduced in order to find out the limits of such a negative result. But so far all those results are often presented as a proof of the great expected difficulties we always shall find pursuing a joint group decision from different individual opinions, if we pursue rational and ethical procedures. In this paper we shall review some of the alternative approaches fuzzy sets theory allows, showing among other things that the main assumption of Arrow's model, not being made explicit in his famous theorem, was its underlying binary logic (a crisp definition is implied in preferences, consistency, liberty, equality, consensus and every concept or piece of information). Moreover, we shall also point out that focusing the problem on the choice issue can be also misleading, at least when dealing with human behaviour.

Item Type: | Article |
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Uncontrolled Keywords: | Fuzzy preferences; Group decision making; Social choice |

Subjects: | Sciences > Statistics > Game theory |

ID Code: | 16313 |

References: | Amo A, Montero J, Molina E (2001) Representation of consistent recursive ules. Eur J Oper Res 130:29–53 Arrow KJ (1951,1964) Social choice and individual values.Wiley, New York Aubin JP (1981) Cooperative fuzzy games. Math Oper Res 6:1–13 Black D (1958) The theory of commitees and elections. Cambridge University Press, Cambridge Bouyssou D, Marchant T, Pirlot M, Perny P, Tsoukias A, Vincke P (2000) Evaluation models: a critical perspective. Kluwer, Boston Brans JP (1998) The DGS Prometee procedure. J Decis Syst 7:283–307 Calvo T, Mayor G, Mesiar R (2002) Aggregation operators. Physica-Verlag, Heidelberg Cutello V, Montero J (1993) A characterization of rational amalgamation operations. Int J Approx Reason 8:325–344 Cutello V, Montero J (1994a) Fuzzy rationality measures. Fuzzy Sets Syst 62:39–44 Cutello V, Montero J (1994b) Hierarchies of aggregation operators. Int J Intell Syst 9:1025–1045 Cutello V, Montero J (1995) Recursive connective rules. Int J Intell Syst 14:3–20 Delgado M, Herrera F, Herrera-Viedma E, Martinez L (1998) Combining numerical and linguistic information in group decision making.Inf Sci 107:177–194 Dubois D, Koning JL (1991) Social choice axioms for fuzzy set aggregation.Fuzzy Sets Syst 43:257–274 Dubois D, Fargier H, Perny P, Prade H (2003) A characterization of generalized concordance rules in multicriteria decision making.Int J Intell Syst 18:751–774 Fedrizzi M (1990) On a consensus measure in a group MCDM problem. In: Kacprzyk J, Fedrizzi M (eds) Multiperson decision making using fuzzy sets and posibility theory. Kluwer, Dordrecht,pp 231–241 Fodor J, Roubens M (1994) Fuzzy preference modelling and multicriteria decision support. Kluwer, Dorcrecht Fung LW, Fu KS (1975) An axiomatic approach to rational decision making in a fuzzy environment. In: Zadeh LA et al (eds) Fuzzy sets and their applications to cognitive and decision processes.Academic, New York, pp 227–256 Gomez D, Montero J (2004) A discussion on aggregation operators.Kybernetika 40:107–120 Herrera F,Martinez L, Sanchez PJ (2007) Managing non-homogeneous information in group decision making. Eur J Oper Res (in press) Kelly JS (1975) Arrow impossibility theorems. Academic, New York Klement EP, Mesiar R, Pap E (2000) Triangular norms. Kluwer, Dordrecht Montero J (1985) A note on Fung-Fu’s theorem. Fuzzy Sets Syst 13:259–269 Montero J (1987a) Arrow’s theorem under fuzzy rationality. Behav Sci 32:267–273 Montero J (1987b) Social welfare functions in a fuzzy environment.Kybernetes 16:241–245 Montero J (1988) Aggregation of fuzzy opinions in a non-homogeneous group. Fuzzy Sets Syst 25:15–20 Montero J (1990) Single-peakedness in weigthed aggregation of fuzzy opinions in a fuzzy group. In: Kacprzyk J,Fedrizzi M (eds)Multiperson decision making using fuzzy sets and posibility theory.Kluwer, Dordrecht, pp 163–171 Montero J (2003) Classifiers and decision makers. In:RuanDet al (eds)Applied computational intelligence. World Scientific, Singapore,pp 19–24 Montero J, Mendel M (1998) Crisp acts, fuzzy decisions. In: Barro S et al (eds) Advances in fuzzy logic. Universidad de Santiago de Compostela, pp 219–238 Montero J, Tejada J, Cutello V (1997) A general model for deriving preference structures from data. Eur J Oper Res 98:98–110 Owen G (1982) Game theory. Academic, New York Pachon JG, Gomez D, Montero J, Yanez J (2003) Searching for the dimension of valued preference relations. Int J Approx Reason 33:133–157 Pattanaik PK (1971) Voting and collective choice. Cambridge University Press, Cambridge Roy B (1993) Decision sciences or decision aid sciences. Eur J Oper Res 66:184–203 Sen AK (1970) Collective choice and social welfare. Holden-Day, San Francisco Shaffer G (1986) Savage revisited. Stat Sci 1:463–501 Weymark JA (1984) Arrow’s theorem with social quasy-orderings.Public Choice 42:235–246 Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353 Zadeh LA (1975) The concept of a linguistic variable and its applications to approximate reasoning. Inf Sci 8:199–249 |

Deposited On: | 12 Sep 2012 11:17 |

Last Modified: | 16 Sep 2015 08:24 |

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