Some novel approaches on the $(\overline{N},p,q)$ summability of double sequences of fuzzy numbers and its applications

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.