The Bounds On The Rate Of Uniform Convergence Of The Fuzzy Learning Processes

This paper mainly investigates the bounds on the rate of uniform convergence of the fuzzy learning processes. Firstly, we discuss the properties of function of fuzzy random variable and that of d metric; Secondly, According to the situation that quantity of loss function sets can be divided into two parts ─finite case and infinite case, the bounds on the rate of uniform convergence of the fuzzy learning processes are proposed respectively, and the relations between these bounds and the capacity and the annealed entropy and VC dimension are provided; Finally, we give a special example to show the sameness between the bounds in this paper and those in the statistical learning theory when fuzzy random samples reduce to random samples.