On a Graded Version of Stochastic Dominance

  1. Pérez-Fernández, Raúl 1
  2. Baz, Juan 1
  3. Díaz, Irene 1
  4. Montes, Susana 1
  1. 1 Universidad de Oviedo
    info

    Universidad de Oviedo

    Oviedo, España

    ROR https://ror.org/006gksa02

Actas:
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) - Atlantis Studies in Uncertainty Modelling

Editorial: Atlantis Press

ISSN: 2589-6644

Año de publicación: 2021

Páginas: 494-500

Congreso: 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)

Tipo: Aportación congreso

DOI: 10.2991/ASUM.K.210827.065 GOOGLE SCHOLAR lock_openAcceso abierto editor

Resumen

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.

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Información de financiación

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).

Financiadores

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