On a Graded Version of Stochastic Dominance
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Universidad de Oviedo
info
Publisher: Atlantis Press
ISSN: 2589-6644
Year of publication: 2021
Pages: 494-500
Congress: 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)
Type: Conference paper
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.
Funding information
This research has been partially supported by the Spanish Ministry of Science and Technology (TIN2017-87600-P and PGC2018-098623-B-I00) and FICYT (FC-GRUPIN-IDI/2018/000176).Funders
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Ministry of Science and Technology
Spain
- TIN2017-87600-P
- PGC2018-098623-B-I00
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FICYT
Spain
- FC-GRUPIN-IDI/2018/000176
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