Applications of N-structures to Fuzzy Graph Theory

Abstract

Fuzzy graphs allow us to model uncertainty and ambiguity near a many of complex networks. In this article, N-fuzzy graphs are analysed, focusing on creating generalized models. To achieve this, we initiate our work by defining N-fuzzy sets before defining N-fuzzy relations to the fundamental structure. The N-fuzzy graphs have N-fuzzy bridges, N-fuzzy cut vertices, and N-fuzzy trees. All structural concepts mentioned were thoroughly assessed. All characterizations and important properties were determined and described, including N-fuzzy bridges, N-fuzzy cut vertices, and N-fuzzy trees. These finding is migrate many classical concepts, which have already been gained from the fields of crisp graphs and fuzzy graphs, to the N-fuzzy encompassing. The findings were clarified by working on specific and generalized examples. The findings gained from this N-fuzzy graph theories can be applied to aiding complex decisions and networks, especially those containing uncertainty and of varying degree systems.