The Choice of an Appropriate Stochastic Order to Aggregate Random Variables

  1. Baz, Juan 1
  2. Díaz, Irene 1
  3. Montes, Susana 1
  1. 1 Universidad de Oviedo
    info

    Universidad de Oviedo

    Oviedo, España

    ROR https://ror.org/006gksa02

Livre:
Building Bridges between Soft and Statistical Methodologies for Data Science

Éditorial: Springer

ISSN: 2194-5357,  2194-5365

ISBN: 9783031155086,  9783031155093

Année de publication: 2022

Pages: 40-47

Type: Chapitre d'ouvrage

DOI: 10.1007/978-3-031-15509-3_6 GOOGLE SCHOLAR

Résumé

Aggregation functions have been widely used as a method to fuse data in a large number of applications. In most of them, the data can be modeled as a simple random sample. Thus, it is reasonable to treat the aggregated values as random variables. In this paper, the concept of aggregation functions of random variables with respect to a stochastic order is presented. Additionally, four alternatives for the choice of the adequate order are considered and their benefits and drawbacks are studied.

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Information sur le financement

This research has been partially supported by the Spanish Ministry of Science and Technology (TIN-2017-87600-P and PGC2018- 098623-B-I00).

Financeurs

Références bibliographiques

  • Bauer, H.: Measure and Integration Theory. De Gruyter, Berlin (2011)
  • Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (2002)
  • De Schuymer, B., De Meyer, H., De Baets, B., Jenei, S.: On the cycle-transitivity of the dice model. Theor. Decis. 54(3), 261–285 (2003)
  • Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions, vol. 127. Cambridge University Press, Cambridge (2009)
  • Kopa, M., Petrová, B.: Strong and weak multivariate first-order stochastic dominance (2018). https://ssrn.com/abstract=3144058
  • Mohd, W.R.W., Abdullah, L.: Aggregation methods in group decision making: a decade survey. Informatica 41(1), 71–86 (2017)
  • Nungesser, M.K., Joyce, L.A., McGuire, A.D.: Effects of spatial aggregation on predictions of forest climate change response. Climate Res. 11(2), 109–124 (1999)
  • Shaked, M., Shanthikumar, J.G.: Stochastic Orders. Springer, New York (2007). https://doi.org/10.1007/978-0-387-34675-5
  • Shanmugam, D., Blalock, D., Balakrishnan, G., Guttag, J.: Better aggregation in test-time augmentation. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 1214–1223 (2021)
  • Zimmermann, H.J.: Fuzzy set theory. WIREs Comput. Stat. 2(3), 317–332 (2010)