Graphical interpretation of the twofold integral and its generalization
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Lower integrals and upper integrals with respect to nonadditive set functions
Fuzzy Sets and Systems
Projection with Double Nonlinear Integrals for Classification
ICDM '08 Proceedings of the 8th industrial conference on Advances in Data Mining: Medical Applications, E-Commerce, Marketing, and Theoretical Aspects
An Optimization-Based Classification Approach with the Non-additive Measure
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
Polynomial Nonlinear Integrals
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks
L1-norm Regularization Based Nonlinear Integrals
ISNN '09 Proceedings of the 6th International Symposium on Neural Networks on Advances in Neural Networks
Real-valued Choquet integrals with fuzzy-valued integrand
Fuzzy Sets and Systems
Fuzzy numbers and fuzzification of the Choquet integral
Fuzzy Sets and Systems
Applying fuzzy measures and nonlinear integrals in data mining
Fuzzy Sets and Systems
Resource-aware secure ECG healthcare monitoring through body sensor networks
IEEE Wireless Communications
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
Data Mining on DNA Sequences of Hepatitis B Virus
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Particle swarm optimization for determining fuzzy measures from data
Information Sciences: an International Journal
Choquet integrals with respect to fuzzy measure on fuzzy σ-algebra
ICMLC'05 Proceedings of the 4th international conference on Advances in Machine Learning and Cybernetics
Modeling decisions for artificial intelligence: theory, tools and applications
MDAI'05 Proceedings of the Second international conference on Modeling Decisions for Artificial Intelligence
A hybrid nonlinear classifier based on generalized choquet integrals
CASDMKM'04 Proceedings of the 2004 Chinese academy of sciences conference on Data Mining and Knowledge Management
Generalized nonlinear classification model based on cross-oriented choquet integral
MLDM'12 Proceedings of the 8th international conference on Machine Learning and Data Mining in Pattern Recognition
Real-valued Choquet integrals for set-valued mappings
International Journal of Approximate Reasoning
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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A new method based on nonlinear integral projections for classification is presented. The contribution rate of each combination of the feature attributes, including each singleton, toward the classification is represented by a fuzzy measure. The nonadditivity of the fuzzy measure reflects the interactions among the feature attributes. The weighted Choquet integral with respect to the fuzzy measure serves as an aggregation tool to project the feature space onto a real axis optimally according to an error criterion, and the classifying attribute is properly numerical analysed on the axis simultaneously making the classification simple. To implement the classification, we need to determine the unknown parameters, the values of fuzzy measure and the weight function. This can be done by running an adaptive genetic algorithm on the given training data. The new classifier is tested by recovering the preset parameters from a set of artificial training data generated from these parameters. It also performs well on several real-world data sets. Beyond discriminating classes, this method can also learn the scaling requirements and the respective importance indexes of the feature attributes as well as the relationships among them. A comprehensive discussion on the semantic and geometric meanings of the parameters is given. Moreover, we show how these parameters' values can be used for short-listing important feature attributes to reduce the complexity (dimensions) of the classification problem. Our new method also compares favorably with other methods on some well-known real-world benchmarks.