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A note on product-sum of \(L\)-\(R\) fuzzy numbers. (English) Zbl 0844.04005
Summary: E. Triesch [ibid. 53, 189-192 (1993)] provided a partial answer to R. Fullér’s [ibid. 41, 83-87 (1991; Zbl 0725.04002)] question about the membership function of the finite sum (defined via the sup-product-norm convolution) of \(L\)-\(R\) fuzzy numbers. In this short note, we prove the other half.

03E72 Theory of fuzzy sets, etc.
26E50 Fuzzy real analysis
Full Text: DOI
[1] Dubois, D.; Prade, H., Additions of interactive fuzzy numbers, IEEE trans. automat. control, 26, 926-936, (1981)
[2] Fullér, R., On product-sum of triangular fuzzy numbers, Fuzzy sets and systems, 41, 83-87, (1991) · Zbl 0725.04002
[3] Triesch, E., On the convergence of product-sum series of L-R fuzzy numbers, Fuzzy sets and systems, 53, 189-192, (1993) · Zbl 0874.26019
[4] Wheeden, R.L.; Zygmund, A., Measure and integral, (1977), Marcel Dekker New York
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