On the convergence of \(T\)-sum of \(L\)-\(R\) fuzzy numbers. (English) Zbl 0844.04004

Summary: 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 \(0\leq r\leq 2\), which generalizes R. Fullér’s results [ibid. 41, 83-87 (1991; Zbl 0725.04002) and ibid. 42, 205-212 (1991; Zbl 0734.04004)] in the case \(r\in \{0, 1, 2\}\).


03E72 Theory of fuzzy sets, etc.
40A99 Convergence and divergence of infinite limiting processes
26E50 Fuzzy real analysis
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