## A note to the $$T$$-sum of $$L$$-$$R$$ fuzzy numbers.(English)Zbl 0871.04010

Summary: We generalize the results of D. H. Hong and S. Y. Hwang [ibid. 63, No. 2, 175-180 (1994; Zbl 0844.04004)] for the membership function of finite (infinite) sum of $$L$$-$$R$$ fuzzy numbers, where the sum is based on some continuous Archimedean $$t$$-norm $$T$$.

### MSC:

 3e+72 Theory of fuzzy sets, etc.

Zbl 0844.04004
Full Text:

### References:

 [1] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press: Academic Press New York · Zbl 0444.94049 [2] Fullér, R.; Keresztfalvi, T., t-norm-based addition of fuzzy intervals, Fuzzy Sets and Systems, 51, 155-159 (1992) [3] Hong, D. H.; Hwang, S. Y., On the convergence of $$T$$-sum of $$L-R$$ fuzzy numbers, Fuzzy Sets and Systems, 63, 175-180 (1994) · Zbl 0844.04004 [5] Schweizer, B.; Sklar, A., Probabilistic Metric Spaces (1983), Elsevier: Elsevier New York · Zbl 0546.60010 [6] 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
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