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Aggregation theory revisited

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Abstract
The field of aggregation theory aims at formalizing in a mathematical way the process of combining several inputs into a single output, typically both the inputs and the output being elements of a poset. Although the field in itself only dates from the second half of the last century, one could easily trace back further in time prominent examples of aggregation functions. For instance, means were already studied by Cauchy in the early 1820s. Although the most popular aggregation processes have historically been those dealing with real numbers, the interest of practitioners in different types of data is not to be neglected. Some prominent examples are the aggregation of strings, which is nowadays a popular topic for computer scientists and bioinformaticians, and the aggregation of rankings, which has been studied in social choice theory since the eighteenth century. In this article, we propose to abandon the current order-based understanding of an aggregation process and embrace a new geometrically oriented sense upon which a new theory of aggregation could be developed.
Keywords
Standards, Liquids, Mathematics, Extraterrestrial measurements, Bioinformatics, Indexes, Beset, betweenness relation, data aggregation, monotonicity

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Please use this url to cite or link to this publication:

MLA
Perez Fernandez, Raul, and Bernard De Baets. “Aggregation Theory Revisited.” IEEE TRANSACTIONS ON FUZZY SYSTEMS, vol. 29, no. 4, 2021, pp. 797–804, doi:10.1109/TFUZZ.2020.2965904.
APA
Perez Fernandez, R., & De Baets, B. (2021). Aggregation theory revisited. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 29(4), 797–804. https://doi.org/10.1109/TFUZZ.2020.2965904
Chicago author-date
Perez Fernandez, Raul, and Bernard De Baets. 2021. “Aggregation Theory Revisited.” IEEE TRANSACTIONS ON FUZZY SYSTEMS 29 (4): 797–804. https://doi.org/10.1109/TFUZZ.2020.2965904.
Chicago author-date (all authors)
Perez Fernandez, Raul, and Bernard De Baets. 2021. “Aggregation Theory Revisited.” IEEE TRANSACTIONS ON FUZZY SYSTEMS 29 (4): 797–804. doi:10.1109/TFUZZ.2020.2965904.
Vancouver
1.
Perez Fernandez R, De Baets B. Aggregation theory revisited. IEEE TRANSACTIONS ON FUZZY SYSTEMS. 2021;29(4):797–804.
IEEE
[1]
R. Perez Fernandez and B. De Baets, “Aggregation theory revisited,” IEEE TRANSACTIONS ON FUZZY SYSTEMS, vol. 29, no. 4, pp. 797–804, 2021.
@article{8703888,
  abstract     = {The field of aggregation theory aims at formalizing in a mathematical way the process of combining several inputs into a single output, typically both the inputs and the output being elements of a poset. Although the field in itself only dates from the second half of the last century, one could easily trace back further in time prominent examples of aggregation functions. For instance, means were already studied by Cauchy in the early 1820s. Although the most popular aggregation processes have historically been those dealing with real numbers, the interest of practitioners in different types of data is not to be neglected. Some prominent examples are the aggregation of strings, which is nowadays a popular topic for computer scientists and bioinformaticians, and the aggregation of rankings, which has been studied in social choice theory since the eighteenth century. In this article, we propose to abandon the current order-based understanding of an aggregation process and embrace a new geometrically oriented sense upon which a new theory of aggregation could be developed.},
  author       = {Perez Fernandez, Raul and De Baets, Bernard},
  issn         = {1063-6706},
  journal      = {IEEE TRANSACTIONS ON FUZZY SYSTEMS},
  keywords     = {Standards,Liquids,Mathematics,Extraterrestrial measurements,Bioinformatics,Indexes,Beset,betweenness relation,data aggregation,monotonicity},
  language     = {eng},
  number       = {4},
  pages        = {797--804},
  title        = {Aggregation theory revisited},
  url          = {http://dx.doi.org/10.1109/TFUZZ.2020.2965904},
  volume       = {29},
  year         = {2021},
}

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