Uncertain Choices: A Comparison of Fuzzy and Probabilistic Approaches

Martinetti, Davide; Montes, Susana; Díaz, Susana; Baets, Bernard De

doi:10.1007/978-3-642-39165-1_28

Cited by 3 publications

(6 citation statements)

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“…Surprisingly, there appears to be no literature on the comparison between fuzzy and probabilistic choice theory. We recently approached this issue in [18,19,20], where we proved some preliminary results. We followed an intuition proposed by Fishburn in [11], i.e.…”

Section: A Correspondence Between Probabilistic and Fuzzy Choice Funcmentioning

confidence: 82%

Fuzzy and probabilistic choice functions: a new set of rationality conditions

Martinetti¹,

Montes²,

Díaz³

et al. 2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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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.

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Section: A Correspondence Between Probabilistic and Fuzzy Choice Funcmentioning

confidence: 82%

Fuzzy and probabilistic choice functions: a new set of rationality conditions

Martinetti¹,

Montes²,

Díaz³

et al. 2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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“…and it has been extensively used in [13] for the study of the connections between probabilistic and fuzzy choice functions, in the case the t-norm is the product. Inspired by its multiplicative nature and the coincidence that it was working well with the product t-norm, we try to generalize this condition to other t-norms.…”

Section: P(x Y) P(y X) = P (X S) P (Y S) For Any S ∈ Bmentioning

confidence: 99%

“…Following the ideas in [13], we consider the case of a probabilistic choice function P defined over a finite set of alternatives X and we want to construct a fuzzy choice function from it, representing the uncertainty of the probabilistic choice function with the gradualness of a fuzzy choice function. To do this, consider a left-continuous t-norm * and its associated residuum and biresiduum operators.…”

Section: Constructing a Fuzzy Choice Function From A Probabilistic Chmentioning

confidence: 99%

“…For example, in [13] we proved that if the t-norm is the product, then p can be computed as follows:…”

Section: Proposition 2 If Conditions 1 and 2 Are Satisfied By A Probamentioning

confidence: 99%

“…Surprisingly, while the connection between fuzzy preference relations and fuzzy choice functions has been studied in depth, there appears to be no literature on the comparison of fuzzy choice functions and probabilistic choice functions. Recently, we approached this problem and in [13] we proved some preliminary results under the assumption that the t-norm used is the product. An interesting connection between the probabilistic and the fuzzy formalisms was established, in which Luce's Choice Axiom played a key role.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bridging Probabilistic and Fuzzy Approaches to Choice Under Uncertainty

Martinetti¹,

Díaz²,

Montes³

et al. 2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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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.

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