## 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:

 3e+72 Theory of fuzzy sets, etc. 2.6e+51 Fuzzy real analysis

Zbl 0725.04002
Full Text:

### 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
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