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On Arrow-Sen style equivalences between rationality conditions for fuzzy choice functions

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Abstract
The Arrow-Sen Theorem establishes the equivalence between different rationality conditions for a choice function. In this contribution we deal with fuzzy versions of these rationality conditions and we study the connection between them. We recall results found in the literature and we prove that they are valid under weaker conditions. We also present new implications and counterexamples that show that our results cannot be obtained under weaker conditions.
Keywords
REVEALED PREFERENCE, T-NORMS, Arrow-Sen Theorem, Revealed preference, Fuzzy choice function, Rationality

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Please use this url to cite or link to this publication:

Chicago
Martinetti, Davide, Susana Montes, Susana Díaz, and Bernard De Baets. 2014. “On Arrow-Sen Style Equivalences Between Rationality Conditions for Fuzzy Choice Functions.” Fuzzy Optimization and Decision Making 13 (4): 369–396.
APA
Martinetti, D., Montes, S., Díaz, S., & De Baets, B. (2014). On Arrow-Sen style equivalences between rationality conditions for fuzzy choice functions. FUZZY OPTIMIZATION AND DECISION MAKING, 13(4), 369–396.
Vancouver
1.
Martinetti D, Montes S, Díaz S, De Baets B. On Arrow-Sen style equivalences between rationality conditions for fuzzy choice functions. FUZZY OPTIMIZATION AND DECISION MAKING. 2014;13(4):369–96.
MLA
Martinetti, Davide, Susana Montes, Susana Díaz, et al. “On Arrow-Sen Style Equivalences Between Rationality Conditions for Fuzzy Choice Functions.” FUZZY OPTIMIZATION AND DECISION MAKING 13.4 (2014): 369–396. Print.
@article{5796641,
  abstract     = {The Arrow-Sen Theorem establishes the equivalence between different rationality conditions for a choice function. In this contribution we deal with fuzzy versions of these rationality conditions and we study the connection between them. We recall results found in the literature and we prove that they are valid under weaker conditions. We also present new implications and counterexamples that show that our results cannot be obtained under weaker conditions.},
  author       = {Martinetti, Davide and Montes, Susana and D{\'i}az, Susana and De Baets, Bernard},
  issn         = {1568-4539},
  journal      = {FUZZY OPTIMIZATION AND DECISION MAKING},
  language     = {eng},
  number       = {4},
  pages        = {369--396},
  title        = {On Arrow-Sen style equivalences between rationality conditions for fuzzy choice functions},
  url          = {http://dx.doi.org/10.1007/s10700-014-9187-z},
  volume       = {13},
  year         = {2014},
}

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