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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.

MSC:

03E72 Theory of fuzzy sets, etc.
26E50 Fuzzy real analysis

Citations:

Zbl 0725.04002
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References:

[1] Dubois, D.; Prade, H., Additions of interactive fuzzy numbers, IEEE Trans. Automat. Control, 26, 926-936 (1981) · Zbl 1457.68262
[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: Marcel Dekker New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.