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

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Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 300))

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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.

The research reported in this paper has been partially supported by project MTM2010-17844 and the Foundation for the promotion in Asturias of the scientific and technolologic research BP10-090.

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Author information

Authors and Affiliations

  1. Dept. Statistics and O.R., University of Oviedo, Oviedo, Spain

    Davide Martinetti, Susana Montes & Susana Díaz

  2. Dept. Appl. Math., Biometrics and Process Control, University of Ghent, Ghent, Belgium

    Bernard De Baets

Authors
  1. Davide Martinetti
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  2. Susana Montes
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  3. Susana Díaz
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  4. Bernard De Baets
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute — IONA College,, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2012 Springer-Verlag Berlin Heidelberg

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Martinetti, D., Montes, S., Díaz, S., De Baets, B. (2012). Some Comments to the Fuzzy Version of the Arrow-Sen Theorem. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8_30

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  • DOI: https://doi.org/10.1007/978-3-642-31724-8_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31723-1

  • Online ISBN: 978-3-642-31724-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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