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Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

Author

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  • Armajac Raventós-Pujol

    (Institute for Advanced Research in Business and Economics and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain)

  • María J. Campión

    (Institute for Advanced Research in Business and Economics and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain)

  • Esteban Induráin

    (Institute for Advanced Materials and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain)

Abstract

We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.

Suggested Citation

  • Armajac Raventós-Pujol & María J. Campión & Esteban Induráin, 2020. "Decomposition and Arrow-Like Aggregation of Fuzzy Preferences," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:436-:d:333580
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    References listed on IDEAS

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