Analysis of approximation of continuous fuzzy functions by multivariate fuzzy polynomials

Abstract

For the given fuzzy valued function J : R n→ F 0( R) , the fuzzy valued Bernstein polynomial is introduced to show the fact that continuous fuzzy valued functions can be approximately represented as the fuzzy valued polynomials on any compact set U⊂ R n . Some equivalent conditions for the continuous fuzzy function F : F 0( R) n→ F 0( R) that can be approximated to any degree of accuracy by fuzzy polynomials on arbitrary compact set U⊂ F 0( R) n are presented.