A note on the finite T-sum of L − R fuzzy numbers and further considerations.

In the first part of this paper we consider the α -cut of a sum of two fuzzy sets. We show that the α -cut of such a sum can be written as one closed interval determined by the minimum and maximum of some special functions, over a set uniquely determined by the considered t -norm. In the second part of the paper we show that not only α -cut of a sum of two fuzzy intervals has this property, but also α -cut of a continuous function of two variables, strictly increasing in each argument as well. Two examples of the presented theory are considered. [ABSTRACT FROM AUTHOR]