Functions approximating by neural networks and fuzzy systems

The survey is given of some results related to approximating the functions of one and of multiple real variables. Several theorems are given of one of the classical approaches – approximating the functions by algebraic polynomials. First results on functions approximating by neural networks and fuzzy systems appeared as an answer to the significant for practical tasks question on possibility of approximating continuous functions in such ways. Later, these fields developed the same way the theory of functions approximating by algebraic polynomials did. Some results are presented, related to functions approximating by neural networks and fuzzy systems.