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Fuzzy Group Identification Problems

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  • Federico Fioravanti
  • Fernando Tohm'e

Abstract

We present a fuzzy version of the Group Identification Problem ("Who is a J?") introduced by Kasher and Rubinstein (1997). We consider a class $N = \{1,2,\ldots,n\}$ of agents, each one with an opinion about the membership to a group J of the members of the society, consisting in a function $\pi : N \to [0; 1]$, indicating for each agent, including herself, the degree of membership to J. We consider the problem of aggregating those functions, satisfying different sets of axioms and characterizing different aggregators. While some results are analogous to those of the originally crisp model, the fuzzy version is able to overcome some of the main impossibility results of Kasher and Rubinstein.

Suggested Citation

  • Federico Fioravanti & Fernando Tohm'e, 2019. "Fuzzy Group Identification Problems," Papers 1912.05540, arXiv.org, revised Jul 2021.
    • Handle: RePEc:arx:papers:1912.05540
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    References listed on IDEAS

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    1. Dutta, Bhaskan, 1987. "Fuzzy preferences and social choice," Mathematical Social Sciences, Elsevier, vol. 13(3), pages 215-229, June.
    2. Dimitrov, D.A. & Sung, S.C., 2003. "On the Axiomatic Characterization of "Who is a J?"," Discussion Paper 2003-89, Tilburg University, Center for Economic Research.
    3. Dutta, Bhaskar & Panda, Santosh C. & Pattanaik, Prasanta K., 1986. "Exact choice and fuzzy preferences," Mathematical Social Sciences, Elsevier, vol. 11(1), pages 53-68, February.
    4. Mowaffaq Hajja, 2013. "Some Elementary Aspects of Means," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-9, May.
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    6. Cho, Wonki Jo & Park, Chang Woo, 2018. "Fractional group identification," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 66-75.
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