Journal of Intelligent & Fuzzy Systems 33 (2017) 947–956 DOI:10.3233/JIFS-162211 IOS Press 947 Tauberian conditions for double sequences which are statistically summable (C,1,1) in fuzzy number space Reha Yapalı and ¨ Ozer Talo ∗ Department of Mathematics, Faculty of Science and Letters, Manisa Celal Bayar University, Manisa, Turkey Abstract. In this paper, we introduce the concept of statistical summability (C,1,1) for double sequences in fuzzy number space E n and also we give some Tauberian conditions for double sequences of fuzzy numbers that are statistically summable (C,1,1). Keywords: Double sequence, statistical convergence, fuzzy number, Tauberian conditions 1. Introduction The notion of statistical convergence for double sequences is presented by Mursaleen and Edely [24] and by M´ oricz [22] independently. Tauberian theo- rems for statistically convergent double sequence are given by many researchers [7, 17, 19, 31]. Also, the concept of statistically summability (C,1,1) is defined and necessary conditions under which statistical con- vergence follows from statistical summability (C,1,1) is given by M´ oricz [23]. Chan and Chen [8] extend the results given by Moricz to double sequence that are statistically summable by weighted mean. The concept of fuzzy set is put forward by Lotfi A. Zadeh in [36] as an extension of the concept of clas- sical set, and since then to today researchers have uti- lized the fuzzy sets to cope with problems occuring in many branches of mathematics [13–16, 37] as well as other areas of science. In connection with sequences, authors have defined many classes of sequences ∗ Corresponding author. ¨ Ozer Talo, Department of Mathe- matics, Faculty of Science and Letters, Manisa Celal Bayar University, Manisa, Turkey. Tel.: +90 236 201 32 12; E-mail: ozertalo@hotmail.com. of fuzzy numbers and examined some properties of these classes. Different kinds of summability methods and related Tauberian theorems have been extended to fuzzy analysis [3, 9, 29, 33–35]. Besides various convergence methods for double sequences of fuzzy numbers have been introduced [12, 21, 25, 27]. In particular, the concept of statistical convergence has been extended to double sequences of fuzzy num- bers recently [26]. In this paper, we define the notion of statical summability (C,1,1) for double sequence in E n . Also, we extend the results that were given by M´ oricz [23] to double sequence in E n . 2. Preliminaries In this section, we introduce the basic notions of fuzzy numbers and refer to [4, 6, 18, 32] for more details. Throughout this paper, R is the real line and N denotes the set of all natural numbers. Let K c (R n ) denote the family of all nonempty com- pact convex subsets of R n . If A, B ∈ K c (R n ) and k ∈ R then the operations of addition and scalar mul- tiplication are defined as 1064-1246/17/$35.00 © 2017 – IOS Press and the authors. All rights reserved