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 inflim inf, lim suplim 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 inflim inf (lim suplim sup, resp.) may not exist. Thus we show that if lim inflim inf and lim suplim 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.