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

Hong, Dug Hun; Hwang, Seok Yoon

Fuzzy Sets Syst. 63, No. 2, 175-180 (1994).

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 \(r\in \{0, 1, 2\}\).

MSC:

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

Keywords:

infinite sum of \(L\)-\(R\) fuzzy numbers; Archimedean \(t\)-norm; convergence of \(T\)-sum; sup-\(t\)-convolution; membership function; limit distribution of the Hamacher sum

Citations:

Zbl 0725.04002; Zbl 0734.04004

References:

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