Robust fitting for the Sugeno integral with respect to general fuzzy measures

Gleb Beliakov , Marek Gągolewski , Simon James

Abstract

The Sugeno integral is an expressive aggregation function with potential applications across a range of decision contexts. Its calculation requires only the lattice minimum and maximum operations, making it particularly suited to ordinal data and robust to scale transformations. However, for practical use in data analysis and prediction, we require efficient methods for learning the associated fuzzy measure. While such methods are well developed for the Choquet integral, the fitting problem is more difficult for the Sugeno integral because it is not amenable to being expressed as a linear combination of weights, and more generally due to plateaus and non-differentiability in the objective function. Previous research has hence focused on heuristic approaches or simplified fuzzy measures. Here we show that the problem of fitting the Sugeno integral to data such that the maximum absolute error is minimized can be solved using an efficient bilevel program. This method can be incorporated into algorithms that learn fuzzy measures with the aim of minimizing the median residual. This equips us with tools that make the Sugeno integral a feasible option in robust data regression and analysis. We provide experimental comparison with a genetic algorithms approach and an example in data analysis.

Author Gleb Beliakov - [Deakin University]
Gleb Beliakov,,
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, Marek Gągolewski (FMIS / DIE) - [Instytut Badań Systemowych Polskiej Akademii Nauk]
Marek Gągolewski,,
- Department of Integral Equations
- Instytut Badań Systemowych Polskiej Akademii Nauk
, Simon James - [Deakin University]
Simon James,,
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Journal seriesInformation Sciences, ISSN 0020-0255, e-ISSN 1872-6291
Issue year2020
Vol514
Pages449-461
Publication size in sheets0.6
Keywords in EnglishSugeno integral, Fuzzy measure, Parameter learning, Aggregation functions
ASJC Classification1802 Information Systems and Management; 1702 Artificial Intelligence; 1706 Computer Science Applications; 1712 Software; 2207 Control and Systems Engineering; 2614 Theoretical Computer Science
DOIDOI:10.1016/j.ins.2019.11.024
URL https://www.sciencedirect.com/science/article/pii/S0020025519310692
Languageen angielski
Score (nominal)200
Score sourcejournalList
ScoreMinisterial score = 200.0, 11-08-2020, ArticleFromJournal
Publication indicators Scopus Citations = 1; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 2.636; WoS Impact Factor: 2018 = 5.524 (2) - 2018=5.305 (5)
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