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Bridging probabilistic and fuzzy approaches to choice under uncertainty

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Abstract
Imprecise choices can be described using either a probabilistic or a fuzzy formalism. No relation between them has been studied so far. In this contribution we present a connection between the two formalisms that strongly makes use of fuzzy implication operators and t-norms. In this framework, Luce's Choice Axiom turns out to be a special case when the product t-norm is considered and other similar choice axioms can be stated, according to the t-norm in use. Also a new family of operators for transforming bipolar relations into unipolar ones is presented.
Keywords
Fuzzy choice function, probabilistic choice function, fuzzy implication operator, fuzzy revealed preference, reciprocal relation, bipolar/unipolar scale, RATIONAL CHOICE, REVEALED PREFERENCE

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Citation

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MLA
Martinetti, Davide, et al. “Bridging Probabilistic and Fuzzy Approaches to Choice under Uncertainty.” Advances in Intelligent Systems Research, edited by G Pasi et al., vol. 32, Atlantis Press, 2013, pp. 856–61.
APA
Martinetti, D., Díaz, S., Montes, S., & De Baets, B. (2013). Bridging probabilistic and fuzzy approaches to choice under uncertainty. In G. Pasi, J. Montero, & D. Ciucci (Eds.), Advances in Intelligent Systems Research (Vol. 32, pp. 856–861). Paris, France: Atlantis Press.
Chicago author-date
Martinetti, Davide, Susana Díaz, Susana Montes, and Bernard De Baets. 2013. “Bridging Probabilistic and Fuzzy Approaches to Choice under Uncertainty.” In Advances in Intelligent Systems Research, edited by G Pasi, J Montero, and D Ciucci, 32:856–61. Paris, France: Atlantis Press.
Chicago author-date (all authors)
Martinetti, Davide, Susana Díaz, Susana Montes, and Bernard De Baets. 2013. “Bridging Probabilistic and Fuzzy Approaches to Choice under Uncertainty.” In Advances in Intelligent Systems Research, ed by. G Pasi, J Montero, and D Ciucci, 32:856–861. Paris, France: Atlantis Press.
Vancouver
1.
Martinetti D, Díaz S, Montes S, De Baets B. Bridging probabilistic and fuzzy approaches to choice under uncertainty. In: Pasi G, Montero J, Ciucci D, editors. Advances in Intelligent Systems Research. Paris, France: Atlantis Press; 2013. p. 856–61.
IEEE
[1]
D. Martinetti, S. Díaz, S. Montes, and B. De Baets, “Bridging probabilistic and fuzzy approaches to choice under uncertainty,” in Advances in Intelligent Systems Research, Milan, Italy, 2013, vol. 32, pp. 856–861.
@inproceedings{4413393,
  abstract     = {Imprecise choices can be described using either a probabilistic or a fuzzy formalism. No relation between them has been studied so far. In this contribution we present a connection between the two formalisms that strongly makes use of fuzzy implication operators and t-norms. In this framework, Luce's Choice Axiom turns out to be a special case when the product t-norm is considered and other similar choice axioms can be stated, according to the t-norm in use. Also a new family of operators for transforming bipolar relations into unipolar ones is presented.},
  author       = {Martinetti, Davide and Díaz, Susana and Montes, Susana and De Baets, Bernard},
  booktitle    = {Advances in Intelligent Systems Research},
  editor       = {Pasi, G and Montero, J and Ciucci, D},
  isbn         = {9789078677789},
  issn         = {1951-6851},
  keywords     = {Fuzzy choice function,probabilistic choice function,fuzzy implication operator,fuzzy revealed preference,reciprocal relation,bipolar/unipolar scale,RATIONAL CHOICE,REVEALED PREFERENCE},
  language     = {eng},
  location     = {Milan, Italy},
  pages        = {856--861},
  publisher    = {Atlantis Press},
  title        = {Bridging probabilistic and fuzzy approaches to choice under uncertainty},
  volume       = {32},
  year         = {2013},
}

Web of Science
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