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Abstract
Probabilistic and fuzzy choice theory are used to describe decision situations in which a certain degree of imprecision is involved. In this work we propose a correspondence between probabilistic and fuzzy choice functions, based on implication operators. Given a probabilistic choice function a fuzzy choice function can be constructed and, furthermore, a new set of rationality conditions is proposed. Finally, we prove that under those conditions, the associated fuzzy choice function fulfills desirable rationality properties.
Keywords
Rationality conditions, Probabilistic choice, Fuzzy choice, Individual choice theory, Implication operators, STOCHASTIC REVEALED PREFERENCE, WEAK AXIOM, TRANSITIVITY, DEMAND, BEHAVIOR

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Citation

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

Chicago
Martinetti, Davide, Susana Montes, Susana Díaz, and Bernard De Baets. 2015. “Fuzzy and Probabilistic Choice Functions : a New Set of Rationality Conditions.” In Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology, 89:492–497. Paris, France: Atlantis Press.
APA
Martinetti, D., Montes, S., Díaz, S., & De Baets, B. (2015). Fuzzy and probabilistic choice functions : a new set of rationality conditions. Proceedings of the 2015 conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (Vol. 89, pp. 492–497). Presented at the 16th World congress of the International Fuzzy Systems Association (IFSA) ; 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), Paris, France: Atlantis Press.
Vancouver
1.
Martinetti D, Montes S, Díaz S, De Baets B. Fuzzy and probabilistic choice functions : a new set of rationality conditions. Proceedings of the 2015 conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology. Paris, France: Atlantis Press; 2015. p. 492–7.
MLA
Martinetti, Davide, Susana Montes, Susana Díaz, et al. “Fuzzy and Probabilistic Choice Functions : a New Set of Rationality Conditions.” Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology. Vol. 89. Paris, France: Atlantis Press, 2015. 492–497. Print.
@inproceedings{7258290,
  abstract     = {Probabilistic and fuzzy choice theory are used to describe decision situations in which a certain degree of imprecision is involved. In this work we propose a correspondence between probabilistic and fuzzy choice functions, based on implication operators. Given a probabilistic choice function a fuzzy choice function can be constructed and, furthermore, a new set of rationality conditions is proposed. Finally, we prove that under those conditions, the associated fuzzy choice function fulfills desirable rationality properties.},
  author       = {Martinetti, Davide and Montes, Susana and D{\'i}az, Susana and De Baets, Bernard},
  booktitle    = {Proceedings of the 2015 conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology},
  isbn         = {9789462520776},
  issn         = {1951-6851},
  language     = {eng},
  location     = {Gijon, Spain},
  pages        = {492--497},
  publisher    = {Atlantis Press},
  title        = {Fuzzy and probabilistic choice functions : a new set of rationality conditions},
  volume       = {89},
  year         = {2015},
}

Web of Science
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