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Springer Verlag (Germany), Communications in Computer and Information Science, p. 780-789

DOI: 10.1007/978-3-319-40581-0_63

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Fitting aggregation functions to data: Part II - idempotization

Book chapter published in 2016 by Maciej Bartoszuk, Gleb Beliakov, Marek Gagolewski, Simon James ORCID
This paper was not found in any repository, but could be made available legally by the author.
This paper was not found in any repository, but could be made available legally by the author.

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Abstract

The use of supervised learning techniques for fitting weights and/or generator functions of weighted quasi-arithmetic means – a special class of idempotent and nondecreasing aggregation functions – to empirical data has already been considered in a number of papers. Nevertheless, there are still some important issues that have not been discussed in the literature yet. In the second part of this two-part contribution we deal with a quite common situation in which we have inputs coming from different sources, describing a similar phenomenon, but which have not been properly normalized. In such a case, idempotent and nondecreasing functions cannot be used to aggregate them unless proper preprocessing is performed. The proposed idempotization method, based on the notion of B-splines, allows for an automatic calibration of independent variables. The introduced technique is applied in an R source code plagiarism detection system.