Approximation of fuzzy numbers using Bernstein-Kantorovich operators of max-product kind

Abstract

In this paper, in order to study the approximation of a fuzzy number with support $[x,y]$ by Bernstein-Kantorovich operator of max-product kind, we first extend these operators from interval [0,1] to a compact  interval $[x,y]$.  We evaluate their orders of uniform approximation to a function $\mathcal{F}$ and prove that they preserve quasi-concavity of function $\mathcal{F}$. Besides studying their approximation properties with regard to a fuzzy number, we also prove that  these sequence of operators preserve the core and support of the fuzzy number. Finally we present some graphical representations in order to  show  approximation of a non continuous fuzzy number using these operators.