Abstract
We propose a procedure devoted to the induction of a shadowed set through the post-processing of a fuzzy set, which in turn is learned from labeled data. More precisely, the fuzzy set is inferred using a modified support vector clustering algorithm, enriched in order to optimize the fuzziness grade. Finally, the fuzzy set is transformed into a shadowed set through application of an optimal alpha-cut. The procedure is tested on synthetic and real-world datasets.
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Notes
- 1.
The choice of \(R^2\) and M as names for these symbols is linked to a special role they will play in Sect. 3.
- 2.
Code and data to replicate experiments are available at https://github.com/dariomalchiodi/WILF2018.
- 3.
It is worth highlighting that the learning algorithm of Sect. 3 can in principle be run on objects labeled using more generic membership grades (that is, values belonging to [0, 1]). However, as such a rich information is normally not available in public datasets, all reported experiments rely on crisp membership labels.
- 4.
Ties were resolved in favor of the correct class, when possible.
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Malchiodi, D., Zanaboni, A.M. (2019). Data-Driven Induction of Shadowed Sets Based on Grade of Fuzziness. In: Fullér, R., Giove, S., Masulli, F. (eds) Fuzzy Logic and Applications. WILF 2018. Lecture Notes in Computer Science(), vol 11291. Springer, Cham. https://doi.org/10.1007/978-3-030-12544-8_2
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