The extension of the Knopp core theorem to the sequences of fuzzy numbers

The concept of the core of a sequence of fuzzy numbers has been introduced by Aytar et al. in [The core of a sequence of fuzzy numbers, Fuzzy Sets and Systems, 159(24) (2008) 3369-3379]. Quite recently, some matrix transformations on the classical sets of sequences of fuzzy numbers have been characterized by Talo and Basar in [Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations, Comput. Math. Appl. 58 (2009) 717-733]. In this paper, we have proved a core theorem for sequences of fuzzy numbers which is analogous to the famous Knoop Core Theorem for real sequences. To achieve this goal, we have studied some properties of the lim sup and lim inf of sequences of fuzzy numbers. Also, we have characterized a class of positive regular matrices of fuzzy numbers such that these matrices leave the core of any bounded sequence of fuzzy numbers invariant. (C) 2014 Elsevier Inc. All rights reserved.