A note on the core of fuzzy numbers

Recently, Aytar et al., The core of a sequence of fuzzy numbers, Fuzzy Sets and Systems 159 (2008) 3369–3379 introduced the concept of the core for sequences of fuzzy numbers and gave a characterization for this concept. Aytar also introduced two different definitions of extreme limits ( lim inf , lim sup and Lim inf, Lim sup) for a bounded sequence of fuzzy numbers. According to these definitions, Lim inf (Lim sup, resp.) of a sequence always exists even though lim inf ( lim sup , resp.) may not exist. Thus we show that if lim inf and lim sup exist, then these two definitions are equivalent. We also characterize the core of a sequence in terms of Lim inf and Lim sup. It is analogous to the characterization of the core given by Aytar.