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The Rationality Of Fuzzy Choice Functions

  • 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)

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    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.

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    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

    Volume (Year): 04 (2008)
    Issue (Month): 03 ()
    Pages: 309-327

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    Handle: RePEc:wsi:nmncxx:v:04:y:2008:i:03:p:309-327
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