Abstract
This paper presents the membership function of infinite (or finite) sum (defined by the sup-t-norm convolution) of L- R fuzzy numbers under the conditions of the convexity of additive generators and the concavity of L, R. As an application, we shall calculate the membership function of the limit distribution of the Hamacher sum ( H r -sum for 0 ⩽ r ⩽ 2, which generalizes Fullér's results [ Fuzzy Sets and Systems 41 (1991) 83–87; 42 (1991) 205–212 in the case r ϵ ś0,1,2ś.
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