On using a-cuts to evaluate fuzzy equations

Abstract Consider an equation y = f (x1,…,xn where the extension principle is used to find Y = f( X 1 ,…, X n ) when we subtitute fuzzy numbers X i for the xi, 1⩽i⩽n. If X i (α) denotes an α-cut of X i , then we argue that, for only certain simple equations, will one obtain Y (α) equal to f( X 1 (α),…, X n (α) where f is evaluated using interval arithmetic.