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Aggregation of fuzzy preferences: Some rules of the mean

Author

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  • JosÊ Luis GarcÎa-Lapresta

    () (Universidad de Valladolid, Dep. de EconomÎa Aplicada , Facultad de Ciencias EconÕmicas y Empresariales, 47011 Valladolid, Spain)

  • Bonifacio Llamazares

    () (Universidad de Valladolid, Dep. de EconomÎa Aplicada , Facultad de Ciencias EconÕmicas y Empresariales, 47011 Valladolid, Spain)

Abstract

This paper studies by means of reciprocal fuzzy binary relations the aggregation of preferences when individuals show their preferences gradually. We have characterized neutral aggregation rules through functions from powers of the unit interval in the unit interval. Furthermore, we have determined the neutral aggregation rules that are decomposable and anonymous. In this class of rules, the collective intensity of preference is the arithmetic mean of the values assigned by a function to the individual intensities of preference. We have also considered the neutral aggregation rules based on quasiarithmetic means. We have established that this class of rules generalizes the simple majority, when individuals have ordinary preferences and collective preferences are reciprocal.

Suggested Citation

  • JosÊ Luis GarcÎa-Lapresta & Bonifacio Llamazares, 2000. "Aggregation of fuzzy preferences: Some rules of the mean," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 673-690.
  • Handle: RePEc:spr:sochwe:v:17:y:2000:i:4:p:673-690
    Note: Received: 23 April 1999/Accepted: 25 September 1999
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    1. repec:spr:grdene:v:17:y:2008:i:6:d:10.1007_s10726-008-9108-z is not listed on IDEAS
    2. Maes, Koen C. & Saminger, Susanne & De Baets, Bernard, 2007. "Representation and construction of self-dual aggregation operators," European Journal of Operational Research, Elsevier, vol. 177(1), pages 472-487, February.
    3. Mostapha Diss & Patrizia Pérez-Asurmendi, 2016. "Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support," Group Decision and Negotiation, Springer, vol. 25(5), pages 967-994, September.
    4. Geslin, Stephanie & Salles, Maurice & Ziad, Abderrahmane, 2003. "Fuzzy aggregation in economic environments: I. Quantitative fuzziness, public goods and monotonicity assumptions," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 155-166, April.
    5. Garcia-Lapresta, Jose Luis & Llamazares, Bonifacio, 2001. "Majority decisions based on difference of votes," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 463-481, June.
    6. Llamazares, Bonifacio, 2004. "Simple and absolute special majorities generated by OWA operators," European Journal of Operational Research, Elsevier, vol. 158(3), pages 707-720, November.
    7. Richard Baron & Mostapha Diss & Eric Rémila & Philippe Solal, 2015. "A geometric examination of majorities based on difference in support," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 123-153, June.
    8. repec:spr:grdene:v:19:y:2010:i:6:d:10.1007_s10726-009-9156-z is not listed on IDEAS
    9. Richard Barrett & Maurice Salles, 2006. "Social Choice With Fuzzy Preferences," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 200615, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    10. De Meyer, H. & De Baets, B. & De Schuymer, B., 2007. "On the transitivity of the comonotonic and countermonotonic comparison of random variables," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 177-193, January.
    11. Piggins, Ashley & Duddy, Conal, 2016. "Oligarchy and soft incompleteness," MPRA Paper 72392, University Library of Munich, Germany.
    12. Llamazares, Bonifacio & Pérez-Asurmendi, Patrizia, 2013. "Triple-acyclicity in majorities based on difference in support," MPRA Paper 52218, University Library of Munich, Germany.

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