• Michael B. Gibilisco
  • Annie M. Gowen
  • Karen E. Albert
  • John N. Mordeson
  • Mark J. Wierman
  • Terry D. Clark
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 315)


This concluding chapter provides a summary of the findings from this book. After showing that a fuzzy maximal set exists, a fuzzy aggregation rule was shown to exist which satisfies all five Arrowian conditions including nondictatorship. Although the Gibbard-Satterthwaite Theorem has considered individual fuzzy preferences, this book shows that both individuals and groups can choose alternatives to varying degrees resulting in a social choice that can be both strategy proof and non-dictatorial.Under strict fuzzy preferences, the Median Voter Theorem is shown to hold; however, this is not found under weak fuzzy preferences.


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  1. [Banerjee(1994)]
    Banerjee, A.: Fuzzy preferences and Arrow-type problems. Social Choice and Welfare 11, 121–130 (1994)CrossRefMATHMathSciNetGoogle Scholar
  2. [Billot(1992)]
    Billot, A.: Economic theory of fuzzy equilibria: an axiomatic analysis. Lecture notes in economics and mathematical systems. Springer (1992),
  3. [Dasgupta and Deb(1999)]
    Dasgupta, M., Deb, R.: An impossibility theorem with fuzzy preferences. In: Logic, Game Theory and Social Choice: Proceedings of the International Conference, LGS, vol. 99, pp. 13–16 (1999)Google Scholar
  4. [Duddy et al.(2011)Duddy, Perote-Peña, and Piggins]
    Duddy, C., Perote-Peña, J., Piggins, A.: Arrow’s theorem and max-star transitivity. Social Choice and Welfare 36(1), 25–34 (2011), CrossRefMATHMathSciNetGoogle Scholar
  5. [Dutta(1987)]
    Dutta, B.: Fuzzy preferences and social choice. Mathematical Social Sciences 13(3), 215–229 (1987)CrossRefMATHMathSciNetGoogle Scholar
  6. [Fono and Andjiga(2005)]
    Fono, L.A., Andjiga, N.G.: Fuzzy strict preference and social choice. Fuzzy Sets Syst. 155, 372–389 (2005), Google Scholar
  7. [Fono et al.(2009)Fono, Donfack-Kommogne, and Andjiga]
    Fono, L.A., Donfack-Kommogne, V., Andjiga, N.G.: Fuzzy Arrow-type results without the pareto principle based on fuzzy pre-orders. Fuzzy Sets and Systems 160(18), 2658–2672 (2009)CrossRefMATHMathSciNetGoogle Scholar
  8. [Mordeson and Clark(2009)]
    Mordeson, J.N., Clark, T.D.: Fuzzy Arrow’s theorem. New Mathematics and Natural Computation 5(2), 371–383 (2009), CrossRefMATHMathSciNetGoogle Scholar
  9. [Richardson(1998)]
    Richardson, G.: The structure of fuzzy preferences: Social choice implications. Social Choice and Welfare 15, 359–369 (1998)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Michael B. Gibilisco
    • 1
  • Annie M. Gowen
    • 2
  • Karen E. Albert
    • 3
  • John N. Mordeson
    • 4
  • Mark J. Wierman
    • 5
  • Terry D. Clark
    • 6
  1. 1.New YorkUSA
  2. 2.PapillionUSA
  3. 3.LincolnUSA
  4. 4.Department of Mathematics Creighton UniversityOmahaUSA
  5. 5.Department of Computer Science Creighton UniversityOmahaUSA
  6. 6.Department of Political Science Creighton UniversityOmahaUSA

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