Marková-Stupňanová, Andrea A note to the addition of fuzzy numbers based on a continuous Archimedean t-norm. (English) Zbl 0919.04010 Fuzzy Sets Syst. 91, No. 2, 253-258 (1997). Summary: A simple method of computing the \(T\)-sum of special types of fuzzy numbers is introduced. For the Łukasiewicz t-norm \(T_L\) the proposed method can be applied to the addition of fuzzy numbers with convex membership functions. The classes of fuzzy numbers leading to \(\oplus_T\)-idempotents are studied for continuous t-norms. Cited in 1 ReviewCited in 16 Documents MSC: 03E72 Theory of fuzzy sets, etc. Keywords:fuzzy arithmetic; triangular norms; \(T\)-sum; fuzzy numbers; addition; t-norms PDFBibTeX XMLCite \textit{A. Marková-Stupňanová}, Fuzzy Sets Syst. 91, No. 2, 253--258 (1997; Zbl 0919.04010) Full Text: DOI References: [1] Dubois, D.; Prade, H., Additions of interactive fuzzy numbers, IEEE Trans. Automat. Control, 26, 926-936 (1981) · Zbl 1457.68262 [2] Kolesárová, A., Triangular norm-based additions of fuzzy numbers and preserving of similarity, BUSEFAL, 69, 43-54 (1997) [3] A. Marková, Idempotents of the \(T\); A. Marková, Idempotents of the \(T\) [4] Mesiar, R., A note to the \(T\)-sum of \(L-R\) fuzzy numbers, Fuzzy Sets and Systems, 79, 259-261 (1996) · Zbl 0871.04010 [5] Mesiar, R., Shape preserving additions of fuzzy intervals, Fuzzy Sets and Systems, 86, 73-78 (1997) · Zbl 0921.04002 [6] Schweizer, B.; Sklar, A., Probabilistic Metric Spaces (1983), Elsevier: Elsevier New York · Zbl 0546.60010 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.