Support Vector Machine Based On Trapezoidal Fuzzy Numbers

Support Vector Machine, which is built on Statistical Learning Theory, is a kind of machine learning method. It can effectively deal with small sample and nonlinear problems. The classic support vector machine is established on the real random samples in the probability space. Therefore, it is difficult to deal with learning problems based on non-real random samples in the non-probability space. The trapezoidal fuzzy number sample is one of non-real random samples. This dissertation will discuss the support vector machine base on trapezoidal fuzzy numbers. Firstly, this dissertation integrates the relation knowledge of fuzzy chance constrained programming and the idea of classic support vector machine, gives the definition of strong fuzzy linear separable data, establishes the support vector machines which input data is trapezoidal fuzzy number, gets its clear equivalent type through a hybrid intelligent algorithm and its optimal solution. Experiments show that the proposed algorithm has a high classification accuracy. Furthermore, this dissertation establishes the support vector machines which input data is quasi-linear fuzzy number and which output data is trapezoidal fuzzy number.