Generalized weighted statistical convergence for double sequences of fuzzy numbers and associated Korovkin-type approximation theorem (Q777023)

Summary: We define the notions of weighted \((\lambda,\mu)\)-statistical convergence of order \((\gamma_1,\gamma_2)\) and strongly weighted \((\lambda,\mu)\)-summability of \((\gamma_1,\gamma_2)\) for fuzzy double sequences, where \(0< \gamma_1\), \(\gamma_2 \leq 1\). We establish an inclusion result and a theorem presenting a connection between these concepts. Moreover, we apply our new concept of weighted \((\lambda,\mu)\)-statistical convergence of order \((\gamma_1, \gamma_2)\) to prove Korovkin-type approximation theorem for functions of two variables in a fuzzy sense. Finally, an illustrative example is provided with the help of \(q\)-analogue of fuzzy Bernstein operators for bivariate functions which shows the significance of our approximation theorem.