Key Theorem & Bounds On The Rate Of Uniform Convergence Of Fuzzy Learning Theory

In view of the fuzzy characteristics of real world, fuzzy set theory and statistics with vague data are combined to generalize key theorem and bounds on rate of uniform convergence of learning processes as the base of statistical learning theory in this thesis. Key theorem and bounds on rate of uniform convergence of fuzzy learning theory are given. Setting of the fuzzy learning problem is brought forward; some theorems about functions of fuzzy number and fuzzy random variable are proved; fuzzy risk functionaK fuzzy empirical risk functional and FERM principle are presented; key theorem of fuzzy learning theory is proved; bounds on the rate of uniform convergence of fuzzy learning process are advanced.