THE RATIONALITY OF FUZZY CHOICE FUNCTIONS

John N. Mordeson (), Kiran R. Bhutani () and Terry D. Clark ()
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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

New Mathematics and Natural Computation (NMNC), 2008, vol. 04, issue 03, 309-327

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.

Keywords: Fuzzy choice function; fuzzy maximal subset; rationalizable (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S1793005708001112

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