## Triangular norm-based addition preserving linearity of $$T$$-sums of linear fuzzy intervals.(English)Zbl 0934.03064

The paper examines triangular norm-based addition of trapezoidal fuzzy numbers [cf. A. Marková, Fuzzy Sets Syst. 85, No. 3, 379-384 (1997; Zbl 0904.04007), R. Mesiar, Fuzzy Sets Syst. 86, No. 1, 73-78 (1997; Zbl 0921.04002)]. Families of t-norms are described such that the result of this addition is also a trapezoidal fuzzy number (e.g. every t-norm less than the Łukasiewicz t-norm).

### MSC:

 03E72 Theory of fuzzy sets, etc. 26E50 Fuzzy real analysis 65G30 Interval and finite arithmetic

### Citations:

Zbl 0904.04007; Zbl 0921.04002
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