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A taxonomy of monotonicity properties for the aggregation of multidimensional data

(2019) INFORMATION FUSION. 52. p.322-334
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Abstract
The property of monotonicity, which requires a function to preserve a given order, has been considered the standard in the aggregation of real numbers for decades. In this paper, we argue that, for the case of multidimensional data, an order-based definition of monotonicity is far too restrictive. We propose several meaningful alternatives to this property not involving the preservation of a given order by returning to its early origins stemming from the field of calculus. Numerous aggregation methods for multidimensional data commonly used by practitioners are studied within our new framework.
Keywords
Monotonicity, Aggregation, Multidimensional data, Centroid, Spatial median, WEAK MONOTONICITY, ORTHOGONALIZATION

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Citation

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

MLA
Perez Fernandez, Raul, et al. “A Taxonomy of Monotonicity Properties for the Aggregation of Multidimensional Data.” INFORMATION FUSION, vol. 52, 2019, pp. 322–34.
APA
Perez Fernandez, R., De Baets, B., & Gagolewski, M. (2019). A taxonomy of monotonicity properties for the aggregation of multidimensional data. INFORMATION FUSION, 52, 322–334.
Chicago author-date
Perez Fernandez, Raul, Bernard De Baets, and Marek Gagolewski. 2019. “A Taxonomy of Monotonicity Properties for the Aggregation of Multidimensional Data.” INFORMATION FUSION 52: 322–34.
Chicago author-date (all authors)
Perez Fernandez, Raul, Bernard De Baets, and Marek Gagolewski. 2019. “A Taxonomy of Monotonicity Properties for the Aggregation of Multidimensional Data.” INFORMATION FUSION 52: 322–334.
Vancouver
1.
Perez Fernandez R, De Baets B, Gagolewski M. A taxonomy of monotonicity properties for the aggregation of multidimensional data. INFORMATION FUSION. 2019;52:322–34.
IEEE
[1]
R. Perez Fernandez, B. De Baets, and M. Gagolewski, “A taxonomy of monotonicity properties for the aggregation of multidimensional data,” INFORMATION FUSION, vol. 52, pp. 322–334, 2019.
@article{8626846,
  abstract     = {The property of monotonicity, which requires a function to preserve a given order, has been considered the standard in the aggregation of real numbers for decades. In this paper, we argue that, for the case of multidimensional data, an order-based definition of monotonicity is far too restrictive. We propose several meaningful alternatives to this property not involving the preservation of a given order by returning to its early origins stemming from the field of calculus. Numerous aggregation methods for multidimensional data commonly used by practitioners are studied within our new framework.},
  author       = {Perez Fernandez, Raul and De Baets, Bernard and Gagolewski, Marek},
  issn         = {1566-2535},
  journal      = {INFORMATION FUSION},
  keywords     = {Monotonicity,Aggregation,Multidimensional data,Centroid,Spatial median,WEAK MONOTONICITY,ORTHOGONALIZATION},
  language     = {eng},
  pages        = {322--334},
  title        = {A taxonomy of monotonicity properties for the aggregation of multidimensional data},
  url          = {http://dx.doi.org/10.1016/j.inffus.2019.05.006},
  volume       = {52},
  year         = {2019},
}

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