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Based on the current practice of charging peak demand, an expectation-oriented stochastic model is established for the demand contracting decision of electricity users. The resultant optimization problem is proved to be nonlinear but convex. Thus, the first-order optimality condition of the proposed model, which leads to an integral equation founded on the probability density function of the peak...
The nonadditive set function defined on the power set of all considered feature attributes can describe the interaction among the contributions from various feature attributes towards classification. The Choquet integral with respect to nonadditive set functions then is a proper aggregation tool in classifications with a nonlinear classifying boundary. Regarding the Choquet integral as a nonlinear...
Signed efficiency measures with relevant nonlinear integrals can be used to treat data that have strong interaction among contributions from various attributes towards a certain objective attribute. The Choquet integral is the most common nonlinear integral. The nonlinear multiregression based on the Choquet integral can well describe the nonlinear relation how the objective attribute depends on the...
A detailed discussion on contributions from feature attributes to the classifying attribute in the nonlinear classification model based on the Choquet integral is given in this paper. The work provides a new understanding to the geometric structure of the model with contribution rates from the feature attributes towards the classification, as well as the interaction among them.
Linear programming (LP) based models provide good solutions to classification problem especially when the data is linearly separable. The assumption of LP classification models is: the contributions from all attributes towards the classification model are the sum of contributions of each attribute. This assumption leads to a weakness of LP classification models when data is linearly inseparable. The...
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