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In the theory of fuzzy measures, Choquet integral is one of the most important tools. The calculation of Choquet integral on real line is difficult for many cases such as nonmonotone functions.
H. Mehri-Dehnavi, H. Agahi, R. Mesiar
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Solving nonlinear programming problems based on the Choquet integral by a genetic algorithm
Journal of Intelligent & Fuzzy Systems, 2015Abstract Nonadditive set functions represent contribution rate of individual feature attributes and combinations of feature attributes toward the target. Their nonadditivity describes the interaction among contributions. The generalized weighted Choquet integral with respect to a nonadditive set function serves as an aggregation ...
Naomi Kochi, Zhenyuan Wang
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Efficient and Scalable Nonlinear Multiple Kernel Aggregation Using the Choquet Integral
International Conference on Information Processing and Management of Uncertainty, 2014Previously, we investigated the definition and applicability of the fuzzy integral (FI) for nonlinear multiple kernel (MK) aggregation in pattern recognition. Kernel theory provides an elegant way to map multi-source heterogeneous data into a combined homogeneous (implicit) space in which aggregation can be carried out.
Lequn Hu +3 more
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On pseudo gradient search for solving nonlinear multiregression with the Choquet integral
2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013The objective function in some real optimization problems may not be differentiable with respect to the unknown parameters at some points such that the gradient does not exist at those points. Replacing the classical gradient search, the method of pseudo gradient search has been proposed and used for solving nonlinear optimization problems, such as ...
Bo Guo, Li Zhang-Westman, Zhenyuan Wang
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S. Gal
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Generalized Nonlinear Classification Model Based on Cross-Oriented Choquet Integral
IAPR International Conference on Machine Learning and Data Mining in Pattern Recognition, 2012A generalized nonlinear classification model based on cross-oriented Choquet integrals is presented. A couple of Choquet integrals are used in this model to achieve the classification boundaries which can classify data in such situation as one class surrounding another one in a high dimensional space. The values of unknown parameters in the generalized
Rong Yang, Zhenyuan Wang
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Choquet integral representations of nonlinear filters with applications to ladar image processing
SPIE Proceedings, 1998The paper describes the application of Choquet integral filters to automatic object detection in laser radar (LADAR) imagery. Choquet integrals are nonlinear integrals with respect to non-additive measures. These integrals can be used to represent typical nonlinear filters such as order statistic filters, linear combination of order statistic filters ...
A. K. Hocaoglu, P. Gader
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