The Bounds On The Rate Of Uniform Convergence Of Learning Process On Possibility Spaces

In this paper, the bounds on the rate of uniform convergence of the learning processes on possibility space are discussed based on the classic Statistical Learning Theory. The concepts of possibility space, credibility measure, fuzzy variable, the distribution function of the fuzzy variable, the expected risk and the empirical risk are introduced, and the properties of the credibility measure are given; according to the quantity of the loss functions, the content is divided into two parts including finite case and infinite case, and the bounds on the rate of uniform convergence on possibility space are discussed respectively, then the relations between these bounds and the capacity and the annealed entropy are given. At last the generalization ability of learning machines that implement the ERM principle are reflected.