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Marek Gagolewski
Polish Academy of Sciences
52Publications
8H-index
233Citations
Publications 55
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#1Gleb Beliakov (Deakin University)H-Index: 33
#2Marek Gagolewski (PAN: Polish Academy of Sciences)H-Index: 8
Last.Simon James (Deakin University)H-Index: 15
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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 pro...
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#1Gleb Beliakov (Deakin University)H-Index: 33
#2Marek Gagolewski (PAN: Polish Academy of Sciences)H-Index: 8
Last.Simon James (Deakin University)H-Index: 15
view all 3 authors...
Defined solely by means of order-theoretic operations meet (min) and join (max), weighted lattice polynomial functions are particularly useful for modelling data on an ordinal scale. A special case...
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#1Raúl Pérez-Fernández (UGent: Ghent University)H-Index: 6
#2Bernard De Baets (UGent: Ghent University)H-Index: 59
Last.Marek Gagolewski (PAN: Polish Academy of Sciences)H-Index: 8
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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 aggr...
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#1Lucian Coroianu (University of Oradea)H-Index: 13
#2Marek Gagolewski (Warsaw University of Technology)H-Index: 8
Last.Przemysław Grzegorzewski (Warsaw University of Technology)H-Index: 22
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The problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric is discussed. The results given in Coroianu et al. (Fuzzy Sets Syst 233:26–51, 2013) for the 1-knot fuzzy numbers are generalized for arbitrary n-knot (\(n\ge 2\)) piecewise linear fuzzy numbers. Some results on the existence and properties of the approximation operator are proved. Then, the stability of some fuzzy number characteristics under approximation...
1 CitationsSource
#1Gleb Beliakov (Deakin University)H-Index: 33
#2Marek Gagolewski (PAN: Polish Academy of Sciences)H-Index: 8
Last.Simon James (Deakin University)H-Index: 15
view all 3 authors...
Abstract The Sugeno integral is a function particularly suited to the aggregation of ordinal inputs. Defined with respect to a fuzzy measure, its ability to account for complementary and redundant relationships between variables brings much potential to the field of biomedicine, where it is common for measurements and patient information to be expressed qualitatively. However, practical applications require well-developed methods for identifying the Sugeno integral’s parameters, and this task is...
2 CitationsSource
#1Lucian Coroianu (University of Oradea)H-Index: 13
#2Robert Fullér (Széchenyi István University)H-Index: 31
Last.Simon James (Deakin University)H-Index: 15
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Abstract The constrained ordered weighted averaging (OWA) aggregation problem arises when we aim to maximize or minimize a convex combination of order statistics under linear inequality constraints that act on the variables with respect to their original sources. The standalone approach to optimizing the OWA under constraints is to consider all permutations of the inputs, which becomes quickly infeasible when there are more than a few variables, however in certain cases we can take advantage of ...
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#1Lucian Coroianu (University of Oradea)H-Index: 13
#2Marek Gagolewski (Warsaw University of Technology)H-Index: 8
The problem of penalty-based data aggregation in generic real normed vector spaces is studied. Some existence and uniqueness results are indicated. Moreover, various properties of the aggregation functions are considered.
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#1Marek Gagolewski (Warsaw University of Technology)H-Index: 8
#2Simon James (Deakin University)H-Index: 15
Last.Gleb Beliakov (Deakin University)H-Index: 33
view all 3 authors...
The problem of learning symmetric capacities (or fuzzy measures) from data is investigated toward applications in data analysis and prediction as well as decision making. Theoretical results regarding the solution minimizing the mean absolute error are exploited to develop an exact branch-refine-and-bound-type algorithm for fitting Sugeno integrals (weighted lattice polynomial functions, max–min operators) with respect to symmetric capacities. The proposed method turns out to be particularly sui...
5 CitationsSource
#1Radomír HalašH-Index: 11
#2Marek GagolewskiH-Index: 8
Last.Radko MesiarH-Index: 49
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