Nonlinear Classification by Linear Programming with Signed Fuzzy Measures

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 concept of signed fuzzy measure is introduced and utilized in LP approach in order to enhance the classification power through capturing all possible interactions among any two or more attributes. The use of the Choquet integral with respect to a signed fuzzy measure on LP model is able to separate the data that is finearly inseparable.