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Some Comments to the Fuzzy Version of the Arrow-Sen Theorem

  • Davide Martinetti
  • Susana Montes
  • Susana Díaz
  • Bernard De Baets
Part of the Communications in Computer and Information Science book series (CCIS, volume 300)

Abstract

The Arrow-Sen Theorem is one of the most important results concerning rationality of choice functions. It states that under suitable hypothesis, several definitions of rationality given by different authors can be considered equivalent. Following the same spirit, other authors have proved that further definitions can also be considered equivalent to rationality. In this work we consider the fuzzy version of this problem, using the most general definition of fuzzy choice function possible. Older results are recalled and in many cases improved and also new theorems are proposed.

Keywords

Fuzzy choice function revealed preference rationality Arrow-Sen Theorem 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Davide Martinetti
    • 1
  • Susana Montes
    • 1
  • Susana Díaz
    • 1
  • Bernard De Baets
    • 2
  1. 1.Dept. Statistics and O.R.University of OviedoOviedoSpain
  2. 2.Dept. Appl. Math., Biometrics and Process ControlUniversity of GhentGhentBelgium

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