Extended stability problem for two fuzzy number-valued functional equations

In this manuscript, we focus on the fuzzy numbers related to the theory of functional equations. Using the metric defined on a fuzzy number space, we prove the Hyers-Ulam-Rassias stability (briefly, HUR-stability) of the following fuzzy number-valued functional equations f(alpha x + beta y/2) + f (alpha x + beta y/2) = alpha f(x) and f(Sigma(m )(i=1)a(i)x(i)) = Sigma(m)(i=1) r(i)f(x(i)) where alpha, beta,a(1), ..., a(m), r(1), ..., r(m) are fixed real numbers. The results obtained here are generalizations and extensions of the corresponding results in [10, 15, 24] in some senses.