Sums of fuzzy sets of summands.

We investigate the addition operation on fuzzy numbers with a fuzzy set of summands. This is a natural generalization of the corresponding operation which involves a crisp set of summands. It is shown that the resulting set is a type-2 fuzzy set. We construct a type-2 membership function of this set. The sum type-2 fuzzy set can be decomposed according to secondary membership grades into the corresponding collection of fuzzy numbers. It helps to represent the addition operation on fuzzy numbers with a fuzzy set of summands in a form which is convenient for a proper understanding and applications. Illustrative examples are given. [ABSTRACT FROM AUTHOR]