Some novel approaches on the (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 (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 (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 (Pm) and (Qn) are Tauberian conditions for (N, p, q) summability under some additional conditions. In the sequel, we prove a fuzzy Korovkin-type approximation theorem by using the (N, p, q) summability method for fuzzy positive linear operators.