Zerrin Onder - Department of Mathematics, Faculty of Arts and Sciences, Usak University, ۶۴۰۰۰, Usak, Turkey
Ekrem Savas - Department of Mathematics, Faculty of Arts and Sciences, Usak University, ۶۴۰۰۰, Usak, Turkey
Ibrahim Canak - Department of Mathematics, Faculty of Sciences, Ege University, ۳۵۱۰۰, Izmir, Turkey

In this paper, our aim is to make a novel interpretation of relation between (\overline{N},p,q) method and P-convergence for double sequences of fuzzy numbers. In accordance with this aim, we derive some Tauberian conditions, controlling O-oscillatory behavior of a double sequence of fuzzy numbers in certain senses, from (\overline{N},p,q) summability to P- convergence with some restrictions on the weight sequences. As special cases, we indicate that O-condition of Hardy type with respect to (P_m) and (Q_n) are Tauberian conditions for (\overline{N},p,q) summability under some additional conditions. In the sequel, we prove a fuzzy Korovkin-type approximation theorem by using the (\overline{N},p,q) summability method for fuzzy positive linear operators.

Double sequences of fuzzy numbers, convergence in Pringsheim's sense, (\overline{N}, P, q) summability, regularly varying sequences, slowly decreasing sequences, slowly oscillating sequences, weighted mean summability method, fuzzy Korovkin theory