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The Rationality Of Fuzzy Choice Functions

Author

Listed:
  • JOHN N. MORDESON

    (Department of Mathematics, Creighton University, Omaha, Nebraska 68178, USA)

  • KIRAN R. BHUTANI

    (Department of Mathematics, The Catholic University of America, Washington D. C 20064, USA)

  • TERRY D. CLARK

    (Department of Political Science, Creighton University, Omaha, Nebraska 68178, USA)

Abstract

If we assume that the preferences of a set of political actors are not cyclic, we would like to know if their collective choices are rationalizable. Given a fuzzy choice rule, do they collectively choose an alternative from the set of undominated alternatives? We consider necessary and sufficient conditions for a partially acyclic fuzzy choice function to be rationalizable. We find that certain fuzzy choice functions that satisfy conditions α and β are rationalizable. Furthermore, any fuzzy choice function that satisfies these two conditions also satisfies Arrow and Warp.

Suggested Citation

  • John N. Mordeson & Kiran R. Bhutani & Terry D. Clark, 2008. "The Rationality Of Fuzzy Choice Functions," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 309-327.
    • Handle: RePEc:wsi:nmncxx:v:04:y:2008:i:03:n:s1793005708001112
    DOI: 10.1142/S1793005708001112
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    Cited by:

    1. S. S. Desai & A. S. Desai, 2016. "Quasi-Transitive Rationality of Fuzzy Choice Functions Through Indicators," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 191-208, November.
    2. Santosh Desai & Rupali Potdar, 2016. "Full Rationality of Fuzzy Choice Functions on Base Domain Through Indicators," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 175-189, November.

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