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On a correspondence between probabilistic and fuzzy choice functions

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Abstract
Probabilistic and fuzzy choice functions are used to describe decision situations in which some degree of uncertainty or imprecision is involved. We propose a way to equate these two formalisms by means of residual implication operations. Furthermore, a set of new rationality conditions for probabilistic choice functions is proposed and proved to be sufficient to ensure that the associated fuzzy choice function is rational.
Keywords
Probabilistic choice, Fuzzy choice, Rationality conditions, Individual choice theory, Residual implication operation, STOCHASTIC REVEALED PREFERENCE, SOCIAL CHOICE, WEAK AXIOM, DEMAND, TRANSITIVITY, RATIONALITY, 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. 2018. “On a Correspondence Between Probabilistic and Fuzzy Choice Functions.” Fuzzy Optimization and Decision Making 17 (3): 247–264.
APA
Martinetti, D., Montes, S., Díaz, S., & De Baets, B. (2018). On a correspondence between probabilistic and fuzzy choice functions. FUZZY OPTIMIZATION AND DECISION MAKING, 17(3), 247–264.
Vancouver
1.
Martinetti D, Montes S, Díaz S, De Baets B. On a correspondence between probabilistic and fuzzy choice functions. FUZZY OPTIMIZATION AND DECISION MAKING. 2018;17(3):247–64.
MLA
Martinetti, Davide, Susana Montes, Susana Díaz, et al. “On a Correspondence Between Probabilistic and Fuzzy Choice Functions.” FUZZY OPTIMIZATION AND DECISION MAKING 17.3 (2018): 247–264. Print.
@article{8579006,
  abstract     = {Probabilistic and fuzzy choice functions are used to describe decision situations in which some degree of uncertainty or imprecision is involved. We propose a way to equate these two formalisms by means of residual implication operations. Furthermore, a set of new rationality conditions for probabilistic choice functions is proposed and proved to be sufficient to ensure that the associated fuzzy choice function is rational.},
  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       = {3},
  pages        = {247--264},
  title        = {On a correspondence between probabilistic and fuzzy choice functions},
  url          = {http://dx.doi.org/10.1007/s10700-017-9272-1},
  volume       = {17},
  year         = {2018},
}

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