In this research article, we propose and explore the idea of a L-VI-GNR and several properties of it, taking values in a complete lattice L- satisfying infinite meet distributive law. Also, we demonstrate that the intersection of two L-VI-GNR is also a L-VI-GNR. Furthermore, we discussed the particular case of union of two L-VI-GNR is a L-VI-GNR.

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