Abstract
LetYbe a real separable Banach space and let𝒦CY,d∞be the subspace of all normal fuzzy convex and upper semicontinuous fuzzy sets ofYequipped with the supremum metricd∞. In this paper, we introduce several types of additive fuzzy set-valued functional equations in𝒦CY,d∞. Using the fixed point technique, we discuss the Hyers-Ulam-Rassias stability of three types additive fuzzy set-valued functional equations, that is, the generalized Cauchy type, the Jensen type, and the Cauchy-Jensen type additive fuzzy set-valued functional equations. Our results can be regarded as important extensions of stability results corresponding to single-valued functional equations and set-valued functional equations, respectively.
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