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On the Role of Monometrics in Penalty-Based Data Aggregation

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Abstract
Penalty functions have been a common tool in data aggregation for decades. Unfortunately, although the definition of a penalty function has evolved over the years, the use of penalty functions has been reduced to the aggregation of real numbers. However, in this `era of aggregation,' the need of generalizing the current definition in order to comply with the characteristics of new types of data arises. In this paper, we bring to the attention the notion of betweenness relation and propose to replace the currently required property of quasiconvexity of a penalty function by the compatibility with a betweenness relation. Several construction methods for a penalty function are provided based on the use of a monometric. Interestingly, several prominent data aggregation methods are proved to fit into this new framework for penalty-based data aggregation.
Keywords
Control and Systems Engineering, Computational Theory and Mathematics, Applied Mathematics, Artificial Intelligence

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

MLA
Perez Fernandez, Raul, and Bernard De Baets. “On the Role of Monometrics in Penalty-Based Data Aggregation.” IEEE Transactions on Fuzzy Systems 27 (2019): 1456–1468. Print.
APA
Perez Fernandez, R., & De Baets, B. (2019). On the Role of Monometrics in Penalty-Based Data Aggregation. IEEE Transactions on Fuzzy Systems, 27, 1456–1468.
Chicago author-date
Perez Fernandez, Raul, and Bernard De Baets. 2019. “On the Role of Monometrics in Penalty-Based Data Aggregation.” IEEE Transactions on Fuzzy Systems 27: 1456–1468.
Chicago author-date (all authors)
Perez Fernandez, Raul, and Bernard De Baets. 2019. “On the Role of Monometrics in Penalty-Based Data Aggregation.” IEEE Transactions on Fuzzy Systems 27: 1456–1468.
Vancouver
1.
Perez Fernandez R, De Baets B. On the Role of Monometrics in Penalty-Based Data Aggregation. IEEE Transactions on Fuzzy Systems. 2019;27:1456–68.
IEEE
[1]
R. Perez Fernandez and B. De Baets, “On the Role of Monometrics in Penalty-Based Data Aggregation,” IEEE Transactions on Fuzzy Systems, vol. 27, pp. 1456–1468, 2019.
@article{8626848,
  abstract     = {Penalty functions have been a common tool in data aggregation for decades. Unfortunately, although the definition of a penalty function has evolved over the years, the use of penalty functions has been reduced to the aggregation of real numbers. However, in this `era of aggregation,' the need of generalizing the current definition in order to comply with the characteristics of new types of data arises. In this paper, we bring to the attention the notion of betweenness relation and propose to replace the currently required property of quasiconvexity of a penalty function by the compatibility with a betweenness relation. Several construction methods for a penalty function are provided based on the use of a monometric. Interestingly, several prominent data aggregation methods are proved to fit into this new framework for penalty-based data aggregation.},
  author       = {Perez Fernandez, Raul and De Baets, Bernard},
  issn         = {1063-6706},
  journal      = {IEEE Transactions on Fuzzy Systems},
  keywords     = {Control and Systems Engineering,Computational Theory and Mathematics,Applied Mathematics,Artificial Intelligence},
  pages        = {1456--1468},
  title        = {On the Role of Monometrics in Penalty-Based Data Aggregation},
  url          = {http://dx.doi.org/10.1109/tfuzz.2018.2880716},
  volume       = {27},
  year         = {2019},
}

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