Bridging Probabilistic and Fuzzy Approaches to Choice Under Uncertainty

DOI

10.2991/eusflat.2013.126How to use a DOI?

Keywords

Fuzzy choice function probabilistic choice function fuzzy implication operator fuzzy revealed preference reciprocal relation bipolar/unipolar scale

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.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Davide Martinetti
AU  - Susana Díaz
AU  - Susana Montes
AU  - Bernard De Baets
PY  - 2013/08
DA  - 2013/08
TI  - Bridging Probabilistic and Fuzzy Approaches to Choice Under Uncertainty
BT  - Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)
PB  - Atlantis Press
SP  - 896
EP  - 901
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2013.126
DO  - 10.2991/eusflat.2013.126
ID  - Martinetti2013/08
ER  -