The Bounds On The Rate Of Uniform Convergence Of Learning Processes On Sugeno Measure Space

In view of the existence of a large number of nonadditive set functions in practical application, Statistical Learning Theory (SLT) is further discussed in this thesis on a kind of typical nonadditive measure space-Sugeno measure space, which is wider than probability space. Firstly, we explore some properties of Sugeno measure and give definitions and properties of g_λ random variable and its distribution function, expected value and varianceon Sugeno measure space. Furthermore, Markov's inequality and Hoeffding's inequality on Sugeno measure space are proven. Finally, according to two cases: the given set of loss functions is a set of indicator functions or totally bounded real-valued functions, we present and prove the bounds on the rate of uniform convergence of learning process on Sugeno measure space and provide relations between these bounds and capacity of the set of functions, the theory of bounds is generalized from probability space to Sugeno measure space in essence.