Rough weighted statistical convergence on locally solid Riesz spaces

Since 2001, rough convergence has been discussed in research where the core factor degree of roughness has been treated only as a real number. Instead of analyzing different results based on the same definition, we start with the new flow of ideas to enlarge the spectrum of degree of roughness. As a consequence we invent a new approach to degree of roughness with approximation of neighborhood conception over locally solid Riesz spaces. While we start working with this new definition and scrutinize existing results, many of the earlier results are violated. Naturally our curiosity begins to know that under which condition(s) we may get back either some of the previous results or not? Apart from these, we consider various non-trivial results which enhance and signify the motivation of our paper.