Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)

On a Graded Version of Stochastic Dominance

Authors
Raúl Pérez-Fernández, Juan Baz, Irene Díaz, Susana Montes
Corresponding Author
Raúl Pérez-Fernández
Available Online 30 August 2021.
DOI
https://doi.org/10.2991/asum.k.210827.065How to use a DOI?
Keywords
Stochastic order, Fuzzy order relation, Fuzzy measure, Graded stochastic dominance
Abstract

A random variable is said to stochastically dominate another random variable if the cumulative distribution function of the former is smaller than or equal to the cumulative distribution function of the latter. In this paper, we present a graded version of stochastic dominance by measuring the part of the real line in which the inequality holds. Interestingly, when a finite and non-null supermodular fuzzy measure is considered, this graded version of stochastic dominance is proven to be a fuzzy order relation w.r.t. the Lukasiewicz t-norm. We also discuss the use of the Lebesgue measure for random variables with bounded support and present different alternatives for random variables with unbounded support.

Copyright
© 2021, 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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Cite this article

TY  - CONF
AU  - Raúl Pérez-Fernández
AU  - Juan Baz
AU  - Irene Díaz
AU  - Susana Montes
PY  - 2021
DA  - 2021/08/30
TI  - On a Graded Version of Stochastic Dominance
BT  - Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
PB  - Atlantis Press
SP  - 494
EP  - 500
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.065
DO  - https://doi.org/10.2991/asum.k.210827.065
ID  - Pérez-Fernández2021
ER  -