Series of fuzzy sets

Series of fuzzy sets with weakly closed, weakly compact or compact α -levels are considered. The basic space is Banach space. The subject of this paper is investigation of infinite addition of fuzzy sets and condition when the sum of α -levels is equal to the α -level of the sum. The results in this paper complement and complete some previous results proved by the same authors in Stojaković and Stojaković [Addition and series of fuzzy sets, Fuzzy Sets and Systems 83 (1996) 341–346] for the series with compact α -levels.